7.1 homework answer key

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Answer Key 7.1

• [latex]9+8b^2[/latex]
• [latex]x-5[/latex]
• [latex]5(9x^2-5)[/latex]
• [latex]1+2n^2[/latex]
• [latex]7(8-5p)[/latex]
• [latex]10(5x-8y)[/latex]
• [latex]7ab(1-5a)[/latex]
• [latex]9x^2y^2(3y^3-8x)[/latex]
• [latex]3a^2b(-1+2ab)[/latex]
• [latex]4x^3(2y^2+1)[/latex]
• [latex]5x^2(-1-x-3x^2)\text{ or }-5x^2(1+x+3x^2)[/latex]
• [latex]8n^5(-4n^4+4n+5)[/latex]
• [latex]4(7m^4+10m^3+2)[/latex]
• [latex]2x(-5x^3+10x+6)[/latex]
• [latex]5(6b^9+ab-3a^2)[/latex]
• [latex]3y^2(9y^5+4x+3)[/latex]
• [latex]-8a^2b(6b+7a+7a^3)[/latex]
• [latex]5(6m^6+3mn^2-5)[/latex]
• [latex]5x^3y^2z(4x^5z+3x^2+7y)[/latex]
• [latex]3(p+4q-5q^2r^2)[/latex]
• [latex]3(-6n^5+n^3-7n+1)[/latex]
• [latex]3a^2(10a^6+2a^3+9a+7)[/latex]
• [latex]-10x^{11}(4+2x-5x^2+5x^3)[/latex]
• [latex]4x^2(-6x^4-x^2+3x+1)[/latex]
• [latex]4mn(-8n^7+m^5+3n^3+4)[/latex]
• [latex]2y^7(-5+3y^3-2y^3x-4yx)[/latex]

Intermediate Algebra Copyright © 2020 by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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CHAPTER 7 KEYS:

Reviews & skills keys:.

6 x 2 6 x 2

8 y 2 8 y 2

2 a b 2 a b

3 m 3 n 3 m 3 n

5 m 2 5 m 2

6 ( a + 4 ) 6 ( a + 4 )

2 ( b + 7 ) 2 ( b + 7 )

14 ( x + 1 ) 14 ( x + 1 )

12 ( p + 1 ) 12 ( p + 1 )

8 ( u − 2 ) 8 ( u − 2 )

30 ( y − 2 ) 30 ( y − 2 )

5 ( x 2 − 5 x + 3 ) 5 ( x 2 − 5 x + 3 )

3 ( y 2 − 4 y + 9 ) 3 ( y 2 − 4 y + 9 )

2 x 2 ( x + 6 ) 2 x 2 ( x + 6 )

3 y 2 ( 2 y − 5 ) 3 y 2 ( 2 y − 5 )

2 x ( 10 x 2 − 5 x + 7 ) 2 x ( 10 x 2 − 5 x + 7 )

4 y ( 6 y 2 − 3 y − 5 ) 4 y ( 6 y 2 − 3 y − 5 )

3 y 2 ( 3 x + 2 x 2 + 7 y ) 3 y 2 ( 3 x + 2 x 2 + 7 y )

3 p ( p 2 − 2 p q + 3 q 2 ) 3 p ( p 2 − 2 p q + 3 q 2 )

−8 ( 8 z + 8 ) −8 ( 8 z + 8 )

−9 ( y + 3 ) −9 ( y + 3 )

−4 b ( b − 4 ) −4 b ( b − 4 )

−7 a ( a − 3 ) −7 a ( a − 3 )

( m + 3 ) ( 4 m − 7 ) ( m + 3 ) ( 4 m − 7 )

( n − 4 ) ( 8 n + 5 ) ( n − 4 ) ( 8 n + 5 )

( x + 8 ) ( y + 3 ) ( x + 8 ) ( y + 3 )

( a + 7 ) ( b + 8 ) ( a + 7 ) ( b + 8 )

( x − 5 ) ( x + 2 ) ( x − 5 ) ( x + 2 )

( y + 4 ) ( y − 7 ) ( y + 4 ) ( y − 7 )

( x + 2 ) ( x + 4 ) ( x + 2 ) ( x + 4 )

( y + 3 ) ( y + 5 ) ( y + 3 ) ( y + 5 )

( q + 4 ) ( q + 6 ) ( q + 4 ) ( q + 6 )

( t + 2 ) ( t + 12 ) ( t + 2 ) ( t + 12 )

( x + 4 ) ( x + 15 ) ( x + 4 ) ( x + 15 )

( v + 3 ) ( v + 20 ) ( v + 3 ) ( v + 20 )

( u − 3 ) ( u − 6 ) ( u − 3 ) ( u − 6 )

( y − 7 ) ( y − 9 ) ( y − 7 ) ( y − 9 )

( h − 2 ) ( h + 6 ) ( h − 2 ) ( h + 6 )

( k − 4 ) ( k + 5 ) ( k − 4 ) ( k + 5 )

( x + 2 ) ( x − 6 ) ( x + 2 ) ( x − 6 )

( y + 4 ) ( y − 5 ) ( y + 4 ) ( y − 5 )

( r + 5 ) ( r − 8 ) ( r + 5 ) ( r − 8 )

( s + 2 ) ( s − 5 ) ( s + 2 ) ( s − 5 )

( m + 3 ) ( m + 6 ) ( m + 3 ) ( m + 6 )

( n − 3 ) ( n − 4 ) ( n − 3 ) ( n − 4 )

( u + 4 v ) ( u + 7 v ) ( u + 4 v ) ( u + 7 v )

( x + 6 y ) ( x + 7 y ) ( x + 6 y ) ( x + 7 y )

( a − b ) ( a − 10 b ) ( a − b ) ( a − 10 b )

( m − n ) ( m − 12 n ) ( m − n ) ( m − 12 n )

ⓐ no method ⓑ undo using FOIL ⓒ factor with grouping

ⓐ factor using grouping ⓑ no method ⓒ undo using FOIL

4 ( m + 1 ) ( m − 2 ) 4 ( m + 1 ) ( m − 2 )

5 ( k + 2 ) ( k − 5 ) 5 ( k + 2 ) ( k − 5 )

3 ( r − 1 ) ( r − 2 ) 3 ( r − 1 ) ( r − 2 )

2 ( t − 2 ) ( t − 3 ) 2 ( t − 2 ) ( t − 3 )

5 x ( x − 1 ) ( x + 4 ) 5 x ( x − 1 ) ( x + 4 )

6 y ( y − 2 ) ( y + 5 ) 6 y ( y − 2 ) ( y + 5 )

( a + 1 ) ( 2 a + 3 ) ( a + 1 ) ( 2 a + 3 )

( b + 1 ) ( 4 b + 1 ) ( b + 1 ) ( 4 b + 1 )

( 2 x − 3 ) ( 4 x − 1 ) ( 2 x − 3 ) ( 4 x − 1 )

( 2 y − 7 ) ( 5 y − 1 ) ( 2 y − 7 ) ( 5 y − 1 )

( a − 1 ) ( 8 a + 5 ) ( a − 1 ) ( 8 a + 5 )

( 2 b + 3 ) ( 3 b − 5 ) ( 2 b + 3 ) ( 3 b − 5 )

( 3 x + 2 ) ( 6 x − 5 ) ( 3 x + 2 ) ( 6 x − 5 )

( 3 y + 1 ) ( 10 y − 21 ) ( 3 y + 1 ) ( 10 y − 21 )

5 n ( n − 4 ) ( 3 n − 5 ) 5 n ( n − 4 ) ( 3 n − 5 )

8 q ( q + 6 ) ( 7 q − 2 ) 8 q ( q + 6 ) ( 7 q − 2 )

( x + 2 ) ( 6 x + 1 ) ( x + 2 ) ( 6 x + 1 )

( 2 y + 1 ) ( 2 y + 3 ) ( 2 y + 1 ) ( 2 y + 3 )

( 4 h − 5 ) ( 5 h + 3 ) ( 4 h − 5 ) ( 5 h + 3 )

( q + 4 ) ( 6 q − 5 ) ( q + 4 ) ( 6 q − 5 )

( 2 t + 5 ) ( 5 t − 3 ) ( 2 t + 5 ) ( 5 t − 3 )

( u + 1 ) ( 3 u + 5 ) ( u + 1 ) ( 3 u + 5 )

4 ( 2 x − 3 ) ( 2 x − 1 ) 4 ( 2 x − 3 ) ( 2 x − 1 )

3 ( 3 w − 2 ) ( 2 w − 3 ) 3 ( 3 w − 2 ) ( 2 w − 3 )

( 2 x + 3 ) 2 ( 2 x + 3 ) 2

( 3 y + 4 ) 2 ( 3 y + 4 ) 2

( 8 y − 5 ) 2 ( 8 y − 5 ) 2

( 4 z − 9 ) 2 ( 4 z − 9 ) 2

( 7 x + 6 y ) 2 ( 7 x + 6 y ) 2

( 8 m + 7 n ) 2 ( 8 m + 7 n ) 2

( 8 r + 3 s ) ( 2 r + 3 s ) ( 8 r + 3 s ) ( 2 r + 3 s )

( 3 u + 4 ) ( 3 u + 25 ) ( 3 u + 4 ) ( 3 u + 25 )

2 y ( 2 x − 3 ) 2 2 y ( 2 x − 3 ) 2

3 q ( 3 p + 5 ) 2 3 q ( 3 p + 5 ) 2

( h − 9 ) ( h + 9 ) ( h − 9 ) ( h + 9 )

( k − 11 ) ( k + 11 ) ( k − 11 ) ( k + 11 )

( m − 1 ) ( m + 1 ) ( m − 1 ) ( m + 1 )

( 9 y − 1 ) ( 9 y + 1 ) ( 9 y − 1 ) ( 9 y + 1 )

( 16 m − 5 n ) ( 16 m + 5 n ) ( 16 m − 5 n ) ( 16 m + 5 n )

( 12 p − 3 q ) ( 12 p + 3 q ) ( 12 p − 3 q ) ( 12 p + 3 q )

( 12 − x ) ( 12 + x ) ( 12 − x ) ( 12 + x )

( 13 − p ) ( 13 + p ) ( 13 − p ) ( 13 + p )

( a 2 + b 2 ) ( a + b ) ( a − b ) ( a 2 + b 2 ) ( a + b ) ( a − b )

( x 2 + 4 ) ( x + 2 ) ( x − 2 ) ( x 2 + 4 ) ( x + 2 ) ( x − 2 )

7 x ( y − 5 ) ( y + 5 ) 7 x ( y − 5 ) ( y + 5 )

5 b ( 3 a − 4 ) ( 3 a + 4 ) 5 b ( 3 a − 4 ) ( 3 a + 4 )

8 ( a 2 + 25 ) 8 ( a 2 + 25 )

9 ( 4 y 2 + 9 ) 9 ( 4 y 2 + 9 )

( x + 3 ) ( x 2 − 3 x + 9 ) ( x + 3 ) ( x 2 − 3 x + 9 )

( y + 2 ) ( y 2 − 2 y + 4 ) ( y + 2 ) ( y 2 − 2 y + 4 )

( u − 5 ) ( u 2 + 5 u + 25 ) ( u − 5 ) ( u 2 + 5 u + 25 )

( v − 7 ) ( v 2 + 7 v + 49 ) ( v − 7 ) ( v 2 + 7 v + 49 )

( 4 − 3 x ) ( 16 + 12 x + 9 x 2 ) ( 4 − 3 x ) ( 16 + 12 x + 9 x 2 )

( 3 − 2 y ) ( 9 + 6 y + 4 y 2 ) ( 3 − 2 y ) ( 9 + 6 y + 4 y 2 )

( 2 x − 3 y ) ( 4 x 2 + 6 x y + 9 y 2 ) ( 2 x − 3 y ) ( 4 x 2 + 6 x y + 9 y 2 )

( 10 m − 5 n ) ( 100 m 2 − 50 m n + 25 n 2 ) ( 10 m − 5 n ) ( 100 m 2 − 50 m n + 25 n 2 )

4 ( 5 p + q ) ( 25 p 2 − 5 p q + q 2 ) 4 ( 5 p + q ) ( 25 p 2 − 5 p q + q 2 )

2 ( 6 c + 7 d ) ( 36 c 2 − 42 c d + 49 d 2 ) 2 ( 6 c + 7 d ) ( 36 c 2 − 42 c d + 49 d 2 )

3 a 3 ( a + 6 ) 3 a 3 ( a + 6 )

9 b 5 ( 5 b + 3 ) 9 b 5 ( 5 b + 3 )

( 5 a − 6 ) ( 2 a − 1 ) ( 5 a − 6 ) ( 2 a − 1 )

( 2 x − 3 ) ( 4 x − 3 ) ( 2 x − 3 ) ( 4 x − 3 )

x ( x 2 + 36 ) x ( x 2 + 36 )

3 ( 9 y 2 + 16 ) 3 ( 9 y 2 + 16 )

4 x ( 2 x − 3 ) ( 2 x + 3 ) 4 x ( 2 x − 3 ) ( 2 x + 3 )

3 ( 3 y − 4 ) ( 3 y + 4 ) 3 ( 3 y − 4 ) ( 3 y + 4 )

( 2 x + 5 y ) 2 ( 2 x + 5 y ) 2

( 3 m + 7 n ) 2 ( 3 m + 7 n ) 2

8 ( y − 1 ) ( y + 3 ) 8 ( y − 1 ) ( y + 3 )

5 ( u − 9 ) ( u + 6 ) 5 ( u − 9 ) ( u + 6 )

2 ( 5 m + 6 ) ( 25 m 2 − 30 m + 36 ) 2 ( 5 m + 6 ) ( 25 m 2 − 30 m + 36 )

3 ( 3 q + 4 ) ( 9 q 2 − 12 q + 16 ) 3 ( 3 q + 4 ) ( 9 q 2 − 12 q + 16 )

4 ( a 2 + 4 ) ( a − 2 ) ( a + 2 ) 4 ( a 2 + 4 ) ( a − 2 ) ( a + 2 )

7 ( y 2 + 1 ) ( y − 1 ) ( y + 1 ) 7 ( y 2 + 1 ) ( y − 1 ) ( y + 1 )

6 ( x + b ) ( x − 2 c ) 6 ( x + b ) ( x − 2 c )

2 ( 4 x − 1 ) ( x + 3 y ) 2 ( 4 x − 1 ) ( x + 3 y )

4 ( p − 1 ) ( p − 3 ) 4 ( p − 1 ) ( p − 3 )

3 ( q − 2 ) ( 2 q + 1 ) 3 ( q − 2 ) ( 2 q + 1 )

x = 3 , x = −5 x = 3 , x = −5

y = 6 , y = −9 y = 6 , y = −9

m = 2 3 , m = − 1 2 m = 2 3 , m = − 1 2

p = − 3 4 , p = 3 4 p = − 3 4 , p = 3 4

u = 0 , u = 1 5 u = 0 , u = 1 5

w = 0 , w = − 3 2 w = 0 , w = − 3 2

x = 1 x = 1

v = 2 v = 2

x = 4 , x = −3 x = 4 , x = −3

b = −2 , b = −7 b = −2 , b = −7

c = 0 , c = 4 3 c = 0 , c = 4 3

d = 3 , d = − 1 2 d = 3 , d = − 1 2

a = 0 , a = −1 a = 0 , a = −1

b = 0 , b = − 1 3 b = 0 , b = − 1 3

p = 7 5 , p = − 7 5 p = 7 5 , p = − 7 5

x = 11 6 , x = − 11 6 x = 11 6 , x = − 11 6

m = 1 , m = 3 2 m = 1 , m = 3 2

k = 3 , k = −3 k = 3 , k = −3

x = 0 , x = 3 2 x = 0 , x = 3 2

y = 0 , y = 1 4 y = 0 , y = 1 4

a = − 5 2 , a = 2 3 a = − 5 2 , a = 2 3

b = 2 , b = 1 20 b = 2 , b = 1 20

−15 , −16 and 15 , 16 −15 , −16 and 15 , 16

−21 , −20 and 20 , 21 −21 , −20 and 20 , 21

5 5 feet and 6 6 feet

12 12 feet and 15 15 feet

5 5 feet and 12 12 feet

24 24 feet and 25 25 feet

Section 7.1 Exercises

8 w 2 8 w 2

2 p q 2 p q

6 m 2 n 3 6 m 2 n 3

5 x 3 5 x 3

4 ( x + 5 ) 4 ( x + 5 )

3 ( 2 m + 3 ) 3 ( 2 m + 3 )

9 ( q + 1 ) 9 ( q + 1 )

8 ( m − 1 ) 8 ( m − 1 )

9 ( n − 7 ) 9 ( n − 7 )

3 ( x 2 + 2 x − 3 ) 3 ( x 2 + 2 x − 3 )

2 ( 4 p 2 + 2 p + 1 ) 2 ( 4 p 2 + 2 p + 1 )

8 y 2 ( y + 2 ) 8 y 2 ( y + 2 )

5 x ( x 2 − 3 x + 4 ) 5 x ( x 2 − 3 x + 4 )

6 y 2 ( 2 x + 3 x 2 − 5 y ) 6 y 2 ( 2 x + 3 x 2 − 5 y )

−2 ( x + 2 ) −2 ( x + 2 )

( x + 1 ) ( 5 x + 3 ) ( x + 1 ) ( 5 x + 3 )

( b − 2 ) ( 3 b − 13 ) ( b − 2 ) ( 3 b − 13 )

( y + 3 ) ( x + 2 ) ( y + 3 ) ( x + 2 )

( u + 2 ) ( v − 9 ) ( u + 2 ) ( v − 9 )

( b − 4 ) ( b + 5 ) ( b − 4 ) ( b + 5 )

( p − 9 ) ( p + 4 ) ( p − 9 ) ( p + 4 )

−10 ( 2 x + 1 ) −10 ( 2 x + 1 )

( x 2 + 2 ) ( 3 x − 7 ) ( x 2 + 2 ) ( 3 x − 7 )

( x + y ) ( x + 5 ) ( x + y ) ( x + 5 )

w ( w − 6 ) w ( w − 6 )

Answers will vary.

Section 7.2 Exercises

( x + 1 ) ( x + 3 ) ( x + 1 ) ( x + 3 )

( m + 1 ) ( m + 11 ) ( m + 1 ) ( m + 11 )

( a + 4 ) ( a + 5 ) ( a + 4 ) ( a + 5 )

( p + 5 ) ( p + 6 ) ( p + 5 ) ( p + 6 )

( n + 3 ) ( n + 16 ) ( n + 3 ) ( n + 16 )

( a + 5 ) ( a + 20 ) ( a + 5 ) ( a + 20 )

( x − 2 ) ( x − 6 ) ( x − 2 ) ( x − 6 )

( y − 3 ) ( y − 15 ) ( y − 3 ) ( y − 15 )

( x − 1 ) ( x − 7 ) ( x − 1 ) ( x − 7 )

( p − 1 ) ( p + 6 ) ( p − 1 ) ( p + 6 )

( y + 1 ) ( y − 7 ) ( y + 1 ) ( y − 7 )

( x − 4 ) ( x + 3 ) ( x − 4 ) ( x + 3 )

( a − 7 ) ( a + 4 ) ( a − 7 ) ( a + 4 )

( w − 9 ) ( w + 4 ) ( w − 9 ) ( w + 4 )

( x − 4 ) ( x − 2 ) ( x − 4 ) ( x − 2 )

( x − 12 ) ( x + 1 ) ( x − 12 ) ( x + 1 )

( p + q ) ( p + 2 q ) ( p + q ) ( p + 2 q )

( r + 3 s ) ( r + 12 s ) ( r + 3 s ) ( r + 12 s )

( m − 2 n ) ( m − 10 n ) ( m − 2 n ) ( m − 10 n )

( x + 8 y ) ( x − 10 y ) ( x + 8 y ) ( x − 10 y )

( m + n ) ( m − 65 n ) ( m + n ) ( m − 65 n )

( a + 8 b ) ( a − 3 b ) ( a + 8 b ) ( a − 3 b )

( u − 6 ) ( u − 6 ) ( u − 6 ) ( u − 6 )

( x + 2 ) ( x − 16 ) ( x + 2 ) ( x − 16 )

( r − 4 s ) ( r − 16 s ) ( r − 4 s ) ( r − 16 s )

( k + 4 ) ( k + 30 ) ( k + 4 ) ( k + 30 )

( m + 8 n ) ( m − 7 n ) ( m + 8 n ) ( m − 7 n )

( u − 15 v ) ( u − 2 v ) ( u − 15 v ) ( u − 2 v )

( x + 8 ) ( x − 7 ) ( x + 8 ) ( x − 7 )

Answers may vary

Section 7.3 Exercises

ⓐ factor the GCF, binomial ⓑ Undo FOIL ⓒ factor by grouping

ⓐ undo FOIL ⓑ factor by grouping ⓒ factor the GCF, binomial

5 ( x + 1 ) ( x + 6 ) 5 ( x + 1 ) ( x + 6 )

2 ( z − 4 ) ( z + 3 ) 2 ( z − 4 ) ( z + 3 )

7 ( v − 1 ) ( v − 8 ) 7 ( v − 1 ) ( v − 8 )

p ( p − 10 ) ( p + 2 ) p ( p − 10 ) ( p + 2 )

3 m ( m − 5 ) ( m − 2 ) 3 m ( m − 5 ) ( m − 2 )

5 x 2 ( x − 3 ) ( x + 5 ) 5 x 2 ( x − 3 ) ( x + 5 )

( 2 t + 5 ) ( t + 1 ) ( 2 t + 5 ) ( t + 1 )

( 11 x + 1 ) ( x + 3 ) ( 11 x + 1 ) ( x + 3 )

( 4 w − 1 ) ( w − 1 ) ( 4 w − 1 ) ( w − 1 )

( 3 p − 2 ) ( 2 p − 5 ) ( 3 p − 2 ) ( 2 p − 5 )

( 4 q + 1 ) ( q − 2 ) ( 4 q + 1 ) ( q − 2 )

( 4 p − 3 ) ( p + 5 ) ( 4 p − 3 ) ( p + 5 )

16 ( x − 1 ) ( x − 1 ) 16 ( x − 1 ) ( x − 1 )

10 q ( 3 q + 2 ) ( q + 4 ) 10 q ( 3 q + 2 ) ( q + 4 )

( 5 n + 1 ) ( n + 4 ) ( 5 n + 1 ) ( n + 4 )

( 3 z + 1 ) ( 3 z + 4 ) ( 3 z + 1 ) ( 3 z + 4 )

( 2 k − 3 ) ( 2 k − 5 ) ( 2 k − 3 ) ( 2 k − 5 )

( 5 s − 4 ) ( s − 1 ) ( 5 s − 4 ) ( s − 1 )

( 3 y + 5 ) ( 2 y − 3 ) ( 3 y + 5 ) ( 2 y − 3 )

( 2 n + 3 ) ( n − 15 ) ( 2 n + 3 ) ( n − 15 )

10 ( 6 y − 1 ) ( y + 5 ) 10 ( 6 y − 1 ) ( y + 5 )

3 z ( 8 z + 3 ) ( 2 z − 5 ) 3 z ( 8 z + 3 ) ( 2 z − 5 )

8 ( 2 s + 3 ) ( s + 1 ) 8 ( 2 s + 3 ) ( s + 1 )

12 ( 4 y − 3 ) ( y + 1 ) 12 ( 4 y − 3 ) ( y + 1 )

( 4 y − 7 ) ( 3 y − 2 ) ( 4 y − 7 ) ( 3 y − 2 )

( a − 5 ) ( a + 4 ) ( a − 5 ) ( a + 4 )

( 2 n − 1 ) ( 3 n + 4 ) ( 2 n − 1 ) ( 3 n + 4 )

13 ( z 2 + 3 z − 2 ) 13 ( z 2 + 3 z − 2 )

( x + 7 ) ( x − 4 ) ( x + 7 ) ( x − 4 )

3 p ( p + 7 ) 3 p ( p + 7 )

6 ( r + 2 ) ( r + 3 ) 6 ( r + 2 ) ( r + 3 )

4 ( 2 n + 1 ) ( 3 n + 1 ) 4 ( 2 n + 1 ) ( 3 n + 1 )

( x + 6 ) ( x − 4 ) ( x + 6 ) ( x − 4 )

−16 ( t − 6 ) ( t + 1 ) −16 ( t − 6 ) ( t + 1 )

Answers may vary.

Section 7.4 Exercises

( 4 y + 3 ) 2 ( 4 y + 3 ) 2

( 6 s + 7 ) 2 ( 6 s + 7 ) 2

( 10 x − 1 ) 2 ( 10 x − 1 ) 2

( 5 n − 12 ) 2 ( 5 n − 12 ) 2

( 7 x − 2 y ) 2 ( 7 x − 2 y ) 2

( 5 n + 4 ) ( 5 n + 1 ) ( 5 n + 4 ) ( 5 n + 1 )

( 8 m − 1 ) 2 ( 8 m − 1 ) 2

10 ( k + 4 ) 2 10 ( k + 4 ) 2

3 u ( 5 u − v ) 2 3 u ( 5 u − v ) 2

( x − 4 ) ( x + 4 ) ( x − 4 ) ( x + 4 )

( 5 v − 1 ) ( 5 v + 1 ) ( 5 v − 1 ) ( 5 v + 1 )

( 11 x − 12 y ) ( 11 x + 12 y ) ( 11 x − 12 y ) ( 11 x + 12 y )

( 13 c − 6 d ) ( 13 c + 6 d ) ( 13 c − 6 d ) ( 13 c + 6 d )

( 7 x − 2 ) ( 7 x + 2 ) ( 7 x − 2 ) ( 7 x + 2 ) ( 2 − 7 x ) ( 2 + 7 x ) ( 2 − 7 x ) ( 2 + 7 x )

( 2 z − 1 ) ( 2 z + 1 ) ( 4 z 2 + 1 ) ( 2 z − 1 ) ( 2 z + 1 ) ( 4 z 2 + 1 )

5 ( q − 3 ) ( q + 3 ) 5 ( q − 3 ) ( q + 3 )

6 ( 4 p 2 + 9 ) 6 ( 4 p 2 + 9 )

( x + 5 ) ( x 2 − 5 x + 25 ) ( x + 5 ) ( x 2 − 5 x + 25 )

( z − 3 ) ( z 2 + 3 z + 9 ) ( z − 3 ) ( z 2 + 3 z + 9 )

( 2 − 7 t ) ( 4 + 14 t + 49 t 2 ) ( 2 − 7 t ) ( 4 + 14 t + 49 t 2 )

( 2 y − 5 z ) ( 4 y 2 + 10 y z + 25 z 2 ) ( 2 y − 5 z ) ( 4 y 2 + 10 y z + 25 z 2 )

7 ( k + 2 ) ( k 2 − 2 k + 4 ) 7 ( k + 2 ) ( k 2 − 2 k + 4 )

2 ( 1 − 2 y ) ( 1 + 2 y + 4 y 2 ) 2 ( 1 − 2 y ) ( 1 + 2 y + 4 y 2 )

( 8 a − 5 ) ( 8 a + 5 ) ( 8 a − 5 ) ( 8 a + 5 )

3 ( 3 q − 1 ) ( 3 q + 1 ) 3 ( 3 q − 1 ) ( 3 q + 1 )

( 4 x − 9 ) 2 ( 4 x − 9 ) 2

2 ( 4 p 2 + 1 ) 2 ( 4 p 2 + 1 )

( 5 − 2 y ) ( 25 + 10 y + 4 y 2 ) ( 5 − 2 y ) ( 25 + 10 y + 4 y 2 )

5 ( 3 n + 2 ) 2 5 ( 3 n + 2 ) 2

( 2 w + 15 ) 2 ( 2 w + 15 ) 2

Section 7.5 Exercises

5 x 3 ( 2 x + 7 ) 5 x 3 ( 2 x + 7 )

( y − 3 ) ( y + 13 ) ( y − 3 ) ( y + 13 )

( 2 n − 1 ) ( n + 7 ) ( 2 n − 1 ) ( n + 7 )

a 3 ( a 2 + 9 ) a 3 ( a 2 + 9 )

( 11 r − s ) ( 11 r + s ) ( 11 r − s ) ( 11 r + s )

8 ( m − 2 ) ( m + 2 ) 8 ( m − 2 ) ( m + 2 )

( 5 w − 6 ) 2 ( 5 w − 6 ) 2

( m + 7 n ) 2 ( m + 7 n ) 2

7 ( b + 3 ) ( b − 2 ) 7 ( b + 3 ) ( b − 2 )

3 ( x − 3 ) ( x 2 + 3 x + 9 ) 3 ( x − 3 ) ( x 2 + 3 x + 9 )

( k − 2 ) ( k + 2 ) ( k 2 + 4 ) ( k − 2 ) ( k + 2 ) ( k 2 + 4 )

3 ( 5 p + 4 ) ( q − 1 ) 3 ( 5 p + 4 ) ( q − 1 )

4 ( x + 3 ) ( x + 7 ) 4 ( x + 3 ) ( x + 7 )

u 2 ( u + 1 ) ( u 2 − u + 1 ) u 2 ( u + 1 ) ( u 2 − u + 1 )

10 ( m − 5 ) ( m + 5 ) ( m 2 + 25 ) 10 ( m − 5 ) ( m + 5 ) ( m 2 + 25 )

ⓐ −16 ( t 2 − 5 ) −16 ( t 2 − 5 ) ⓑ −8 ( 2 t + 5 ) ( t − 2 ) −8 ( 2 t + 5 ) ( t − 2 )

Section 7.6 Exercises

x = 3 , x = −7 x = 3 , x = −7

a = 10 / 3 , a = 7 / 2 a = 10 / 3 , a = 7 / 2

m = 0 , m = 5 / 12 m = 0 , m = 5 / 12

y = 3 y = 3

x = 1 / 2 x = 1 / 2

x = −3 , x = −4 x = −3 , x = −4

a = −4 / 5 , a = 6 a = −4 / 5 , a = 6

m = 5 / 4 , m = 3 m = 5 / 4 , m = 3

a = −1 , a = 0 a = −1 , a = 0

m = 12 / 7 , m = −12 / 7 m = 12 / 7 , m = −12 / 7

y = −1 , y = 6 y = −1 , y = 6

x = 3 / 2 , x = −1 x = 3 / 2 , x = −1

p = 0 , p = ¾ p = 0 , p = ¾

x = 3 / 2 x = 3 / 2

7 and 8 ; − 8 and −7 7 and 8 ; − 8 and −7

4 feet and 7 feet 4 feet and 7 feet

6 feet and 8 feet 6 feet and 8 feet

x = −8 , x = 3 x = −8 , x = 3

p = −1 , p = −11 p = −1 , p = −11

m = −2 , m = 8 m = −2 , m = 8

a = 0 , a = −6 , a = 7 a = 0 , a = −6 , a = 7

10 and 11 ; − 11 and −10 10 and 11 ; − 11 and −10

Review Exercises

6 ( 4 x − 7 ) 6 ( 4 x − 7 )

3 m 2 ( 5 m 2 + 2 n ) 3 m 2 ( 5 m 2 + 2 n )

( a + b ) ( x − y ) ( a + b ) ( x − y )

( x − 3 ) ( x + 7 ) ( x − 3 ) ( x + 7 )

( m 2 + 1 ) ( m + 1 ) ( m 2 + 1 ) ( m + 1 )

( u + 8 ) ( u + 9 ) ( u + 8 ) ( u + 9 )

( k − 6 ) ( k − 10 ) ( k − 6 ) ( k − 10 )

( y + 7 ) ( y − 1 ) ( y + 7 ) ( y − 1 )

( s − 4 ) ( s + 2 ) ( s − 4 ) ( s + 2 )

( x + 5 y ) ( x + 7 y ) ( x + 5 y ) ( x + 7 y )

( a + 7 b ) ( a − 3 b ) ( a + 7 b ) ( a − 3 b )

Factor the GCF

6 ( x + 2 ) ( x + 5 ) 6 ( x + 2 ) ( x + 5 )

3 n 2 ( n − 8 ) ( n + 4 ) 3 n 2 ( n − 8 ) ( n + 4 )

( x + 4 ) ( 2 x + 1 ) ( x + 4 ) ( 2 x + 1 )

( 3 a − 1 ) ( 6 a − 1 ) ( 3 a − 1 ) ( 6 a − 1 )

( 5 p + 4 ) ( 3 p − 2 ) ( 5 p + 4 ) ( 3 p − 2 )

( 5 s − 2 ) ( 8 s + 3 ) ( 5 s − 2 ) ( 8 s + 3 )

3 ( x + 4 ) ( x − 3 ) 3 ( x + 4 ) ( x − 3 )

5 ( 4 y + 1 ) ( 3 y − 5 ) 5 ( 4 y + 1 ) ( 3 y − 5 )

( 5 x + 3 ) 2 ( 5 x + 3 ) 2

( 6 a − 7 b ) 2 ( 6 a − 7 b ) 2

10 ( 2 x + 9 ) 2 10 ( 2 x + 9 ) 2

2 y ( y − 4 ) 2 2 y ( y − 4 ) 2

( 9 r − 5 ) ( 9 r + 5 ) ( 9 r − 5 ) ( 9 r + 5 )

( 13 m + n ) ( 13 m − n ) ( 13 m + n ) ( 13 m − n )

( 5 p − 1 ) ( 5 p + 1 ) ( 5 p − 1 ) ( 5 p + 1 )

( 3 + 11 y ) ( 3 − 11 y ) ( 3 + 11 y ) ( 3 − 11 y )

5 ( 2 x − 5 ) ( 2 x + 5 ) 5 ( 2 x − 5 ) ( 2 x + 5 )

u ( 7 u + 3 ) ( 7 u − 3 ) u ( 7 u + 3 ) ( 7 u − 3 )

( a − 5 ) ( a 2 + 5 a + 25 ) ( a − 5 ) ( a 2 + 5 a + 25 )

2 ( m + 3 ) ( m 2 − 3 m + 9 ) 2 ( m + 3 ) ( m 2 − 3 m + 9 )

4 x 2 ( 6 x + 11 ) 4 x 2 ( 6 x + 11 )

( 4 n − 7 m ) 2 ( 4 n − 7 m ) 2

( r + 6 ) ( 5 r − 8 ) ( r + 6 ) ( 5 r − 8 )

( n 2 + 9 ) ( n + 3 ) ( n − 3 ) ( n 2 + 9 ) ( n + 3 ) ( n − 3 )

5 ( x − 3 ) ( x + 4 ) 5 ( x − 3 ) ( x + 4 )

( m + 5 ) ( m 2 − 5 m + 25 ) ( m + 5 ) ( m 2 − 5 m + 25 )

a = 3 a = −7 a = 3 a = −7

m = 0 m = 5 2 m = –6 m = 0 m = 5 2 m = –6

x = −4 , x = −5 x = −4 , x = −5

p = − 5 2 , p = 8 p = − 5 2 , p = 8

m = 5 12 , m = − 5 12 m = 5 12 , m = − 5 12

−21 , −22 21 , 22 −21 , −22 21 , 22

Practice Test

7 ( y − 6 ) 7 ( y − 6 )

40 a 2 ( 2 + 3 a ) 40 a 2 ( 2 + 3 a )

( x + 7 ) ( x + 6 ) ( x + 7 ) ( x + 6 )

3 a ( a + 4 ) ( a − 6 ) 3 a ( a + 4 ) ( a − 6 )

5 ( n + 3 ) 2 5 ( n + 3 ) 2

( x − 8 ) ( y + 7 ) ( x − 8 ) ( y + 7 )

( 3 s − 2 ) 2 ( 3 s − 2 ) 2

( 10 − a ) ( 10 + a ) ( 10 − a ) ( 10 + a )

3 ( x + 5 y ) ( x − 5 y ) 3 ( x + 5 y ) ( x − 5 y )

( a − 3 ) ( b − 2 ) ( a − 3 ) ( b − 2 )

( 4 m + 1 ) ( 2 m + 5 ) ( 4 m + 1 ) ( 2 m + 5 )

y = −11 , y = 12 y = −11 , y = 12

b = 1 , b = −1 b = 1 , b = −1

n = − 7 4 , n = −3 n = − 7 4 , n = −3

12 and 13 ; − 13 and −12 12 and 13 ; − 13 and −12

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• Publisher/website: OpenStax
• Book title: Elementary Algebra
• Publication date: Feb 22, 2017
• Location: Houston, Texas
• Book URL: https://openstax.org/books/elementary-algebra/pages/1-introduction
• Section URL: https://openstax.org/books/elementary-algebra/pages/chapter-7

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Texas Go Math Grade 7 Lesson 7.1 Answer Key Linear Relationships in the Form y = mx + b

Refer to our  Texas Go Math Grade 7 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 7 Lesson 7.1 Answer Key Linear Relationships in the Form y = mx + b.

Texas Go Math Grade 7 Lesson 7.1 Explore Activity Answer Key

Discovering Linear Relationships

Many real-world situations can be described by linear relationships.

Question 1. How much more than $5 does Jodie pay for one ticket? What if she buys 5 tickets? Explain. Answer: Jodie pays $2 more for one ticket. If she buys 5 tickets she will pay also $ 2 more because only at the first payment is charged $ 2.

Lesson 7.1 Modeling Linear Relationships Answer Key Question 2. Analyze Relationships Describe the total amount paid in dollars based on the number of tickets. Answer: One ticket: 2 + 5= 7 Two tickets: 2 – 5 (2) = 12 Three tickets: 2 + 5 (3) = 17 Four tickets: 2 + 5 (4) = 22 Five tickets: 2 + 5 (5) = 27

One ticket cost $7. Two tickets cost $12. Three tickets cost $17. Four tickets cost $ 22. Five tickets $ 27.

A man’s shoe size is approximately 3 times his foot length in inches minus 22. Use a table to represent the relationship between foot length and shoe size.

Question 3. Analyze Relationships If someone had a foot length of 13 inches, how can you use the table to determine his shoe size? Answer: Multiply 13 by 3 and subtract 22 from that product 13 ∙ 3 = 39 39 – 22 = 17

Question 4. Critical Thinking Foot lengths do not have to be whole numbers. Give an example of a non-whole number foot length you could have chosen when filling in the table and find the approximate shoe size. What should a person do if their foot length does not correspond to a whole or half shoe size? Explain. Answer: For example: Foot Length of 12A in. 12.4 ∙ 3 – 22 = 37.2 – 22 = 15.2 therefore, it will be chosen shoe with a size of 15.5. Conclusion: If a number whose decimal is between 0 and 5 is obtained, then foot length corresponds to half shoe size, if a number whose decimal is between 5 and 9 is obtained then foot length corresponds to whole shoe size.

Question 6. Make a Prediction How could you find the amount pledged by Luis’s aunt if Luis walks 7 miles? What is the amount pledged? Answer: If Luis walks 7 miles the amount of pledged will be: 37.5 + 1.5 (2) = $40.5 If Luis walks 7 miles the amount of pledged will be $ 40.5.

The relationship between the cost of an online advertisement for a movie and the number of times it is clicked on is shown in the table.

Question 9. What is the cost for the advertisement if it is clicked 1000 times? Answer: An online advertisement for a movie if it is clicked 1000 times will cost: 150 + 0.5 (1000) = 150 + 500 = $650 An online advertisement for a movie if it is clicked 1000 times will cost $ 650.

Question 10. Is there a lower limit for the number of clicks? Is there an upper limit? Explain. Answer: For every ten clicks, we’re paying half a dollar, dividing that half-dollar difference from 10 to get a one-click cost. \(\frac{0.5}{10}\) = 0.05 The upper limit does not exist because each click increases the price.

Texas Go Math Grade 7 Lesson 7.1 Guided Practice Answer Key

STEP 2: Determine how many more dollars than _________ that it costs to take 3 credits. It costs _________ – _________ = _________ more than _________ to take 3 credits.

STEP 3: Give a verbal description for the relationship between credits and cost. The yearly cost of the community college is _________ plus _________ for each credit taken. Answer: Each value for credits is 3 greater than the previous one. Each value for cost is $75 greater than the previous one. This mean one credit correspond to $25 in cost.

Determine how many more dollars than $75 that it costs to take 3 credits. It cost 175 – 75 = $100 more than $75 to take 3 credits.

The yearly cost of community college is $100 plus $25 for each credit taken.

Essential Question Check-In

Question 3. When using tables and verbal descriptions to describe a linear relationship, why is it useful to convert from one to another? Answer: Because in this way a connection is established and it is clearly explained how the connection has developed between them. It can be concluded quite a lot in case we know the value of one size and its relationship with another to accurately calculate the value of the other.

Texas Go Math Grade 7 Lesson 7.1 Independent Practice Answer Key

A teacher is making multiple copies of a 1 -page homework assignment. The time it takes her in seconds is 2 times the number of copies she makes plus 3. Question 4. What does the 3 represent in this scenario? What does the 2 represent? Answer: This scenario we can represent with next equation: y = 2 ∙ x + 3 Therefore when we look general form y = m ∙ x + b, in our equation m = 2 and b = 3.

Texas Go Math Grade 7 Answers Lesson 7.1 Practice Answers Question 5. What is the total number of seconds it takes for the teacher to make 1 copy? 2 copies? 3 copies? By how many seconds does the total time increase for each copy? Answer: For one copy: x = 1 y = 2 (1) + 3 y = 5 For two copies: x = 2 y = 2 (2) + 3 y = 7 For three copies: x = 3 y = 2 (3) + 3 y = 9 For each subsequent copy, it takes two seconds more.

Question 8. Based on your answer to exercise 7, how many minutes should you receive for inserting 4 dimes? Answer: You should receive 4 ∙ 4 = 16 minutes

Question 9. Analyze Relationships Give a verbal description of the relationship between dimes and the number of minutes left on the meter. Answer: Rosalee has 6 minutes left for parking plus an additional 4 minutes for each dime she adds.

Question 10. Look at your answer for exercise 9. What does each of the numbers in the answer represent? Answer: If we Look at the equation y = m ∙ x + b, for our example m = 16, b = 6, y represent how many minutes left for parking space and x represents how meny dimes are added.

The cost in dollars of a loaf of bread in a bakery is equal to 2 minus 0.25 times the number of days since it was baked. Question 11. What is different about this description compared to most of the other descriptions you have seen in this lesson? Answer: The difference is that in our exercises it was mostly an increase for a certain value. More precisely, we added a new value to the initial value, while in this case we deduct some value from the value.

Question 12. Make a Conjecture Is there a point at which the linear relationship between days and dollars no longer makes sense? Answer: Equation is: y = 2 – 0.25 ∙ x 8 days after being baked, the Linear relationship between days and dollars no longer makes sense, because: y = 2 – 0.25 ∙ 8 = 2 – 2 = 0 y represent the cost in dollars of a loaf of bread and x represent a number of days since it was baked.

Question 14. Find the number of days it will take the price to reach $0.25. Answer: In that case y = 0.25 Replace this in equation y = 2 – 0.25 ∙ x y = 2 – 0.25 ∙ x 0.25 = 2 – 0.25 ∙ x Subtract 2 from each side. 0.25 – 2 = 2 – 0.25 ∙ x – 2 – 1.75 = 0.25 ∙ x Divide both sides by -0.25 \(\frac{-1.75}{-0.25}\) = x 7 = x It will take 7 days for a price to reach $ 0.25.

Question 16. Analyze Relationships Can you give a description of the relationship between the years since the tree was transplanted and its height in inches? If so, what is it? Answer: The tree had a height of 18 in. before it was transplanted and plus an additional 8 in. for each year that follows.

H.O.T. Focus on Higher Order Thinking

Question 17. Communicate Mathematical Ideas Suppose you are analyzing the relationship between time and distance given in a table, and there are 4 values for each quantity. You divide distance 2 minus distance 1 by time 2 minus time 1. You then divide distance 4 minus distance 3 by time 4 minus time-3 and get a different answer. What can you say about the relationship? Explain. Answer: If you get different answers that means its not about equal distance or time given in the table, as in exercise 15.

Question 18. Persevere in Problem-Solving There is a linear relationship between a salesperson’s sales and her weekly income. If her sales are $200, her income is $500, and if her sales are $1,200, her income is $600. What is the relationship between sales and income? Answer: The relationship between sales and income is given by the equation y = \(\frac{1}{10}\) ∙ x + 480 where y represents sales, and x represents income.

Question 19. Critique Reasoning Molly orders necklace kits online. The cost of the necklace kits can be represented by a linear relationship. Molly’s order of 3 kits cost $12.50. Another order of 5 kits cost $17.50. Molly decides that the kits cost $5 each. Is she correct? Explain. Answer: Equation: y = \(\frac{5}{2}\) ∙ x + 5 The procedure for obtaining this equation 5: First find the difference between the number of necklaces in these orders 5 – 3 = 2. Then find the difference between the prices 17.5 – 12.5 = 5 Divide this two values \(\frac{5}{2}\) = 2.5 That much costs one necklace kits The kits cost $ 2.5 each. Molly’s answer is not correct.

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