lesson 6 homework practice add linear expressions answer key

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Glencoe Math Course 2, Grade: 7 Publisher: Glencoe/McGraw-Hill

Glencoe math course 2, title : glencoe math course 2, publisher : glencoe/mcgraw-hill, isbn : not available, isbn-13 : 9780021359141, use the table below to find videos, mobile apps, worksheets and lessons that supplement glencoe math course 2., textbook resources.

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5 m 2 5 m 2

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 )

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

3 y 2 ( 2 y − 5 ) 3 y 2 ( 2 y − 5 )

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

2 a b ( 4 a 2 + a b − 3 b 2 ) 2 a b ( 4 a 2 + a b − 3 b 2 )

−4 b ( b 2 − 4 b + 2 ) −4 b ( b 2 − 4 b + 2 )

−7 a ( a 2 − 3 a + 2 ) −7 a ( a 2 − 3 a + 2 )

( 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 ) ⓑ ( 5 x − 4 ) ( 4 x − 3 ) ( 5 x − 4 ) ( 4 x − 3 )

ⓐ ( y + 4 ) ( y − 7 ) ( y + 4 ) ( y − 7 ) ⓑ ( 7 m − 3 ) ( 6 m − 5 ) ( 7 m − 3 ) ( 6 m − 5 )

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

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

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

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

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

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

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

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

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 )

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

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

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 ( 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 )

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

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

( x − 3 ) ( x − 1 ) ( x − 3 ) ( x − 1 )

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

( 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

2 y ( 2 x − 3 ) 2 2 y ( 2 x − 3 ) 2

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

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

( 11 p − 3 q ) ( 11 p + 3 q ) ( 11 p − 3 q ) ( 11 p + 3 q )

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

7 c 2 ( a − b ) ( a + b ) ( a 2 + b 2 ) 7 c 2 ( a − b ) ( a + b ) ( a 2 + b 2 )

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

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

( 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 )

( 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 )

( −2 y + 1 ) ( 13 y 2 + 5 y + 1 ) ( −2 y + 1 ) ( 13 y 2 + 5 y + 1 )

( −4 n + 3 ) ( 31 n 2 + 21 n + 9 ) ( −4 n + 3 ) ( 31 n 2 + 21 n + 9 )

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

5 y ( y − 9 ) ( y + 6 ) 5 y ( y − 9 ) ( y + 6 )

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 x − 4 y ) 2 ( 3 x − 4 y ) 2

2 x y ( 25 x 2 + 36 ) 2 x y ( 25 x 2 + 36 )

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

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

2 ( p + 3 q ) ( p 2 − 3 p q + 9 q 2 ) 2 ( p + 3 q ) ( p 2 − 3 p q + 9 q 2 )

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

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

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

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

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

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

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

( 4 x − 3 y − 8 ) ( 4 x − 3 y + 8 ) ( 4 x − 3 y − 8 ) ( 4 x − 3 y + 8 )

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

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

c = 2 , c = 4 3 c = 2 , c = 4 3

d = 3 , d = − 1 2 d = 3 , d = − 1 2

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

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

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

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

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

ⓐ x = −3 x = −3 or x = 5 x = 5 ⓑ ( −3 , 7 ) ( −3 , 7 ) ( 5 , 7 ) ( 5 , 7 )

ⓐ x = 1 x = 1 or x = 7 x = 7 ⓑ ( 1 , −4 ) ( 1 , −4 ) ( 7 , −4 ) ( 7 , −4 )

ⓐ x = 1 x = 1 or x = 5 2 x = 5 2 ⓑ ( 1 , 0 ) , ( 1 , 0 ) , ( 5 2 , 0 ) ( 5 2 , 0 ) ⓒ ( 0 , 5 ) ( 0 , 5 )

ⓐ x = −3 x = −3 or x = 5 6 x = 5 6 ⓑ ( −3 , 0 ) , ( −3 , 0 ) , ( 5 6 , 0 ) ( 5 6 , 0 ) ⓒ ( 0 , −15 ) ( 0 , −15 )

−15 , −17 −15 , −17 and 15, 17

−23 , −21 −23 , −21 and 21, 23

The width is 5 feet and length is 6 feet.

The length of the patio is 12 feet and the width 15 feet.

5 feet and 12 feet

24 feet and 25 feet

ⓐ 5 ⓑ 0;3 ⓒ 196

ⓐ 4 ⓑ 0;2 ⓒ 144

Section 6.1 Exercises

2 p q 2 p q

6 m 2 n 3 6 m 2 n 3

5 x 3 y 5 x 3 y

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

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 )

3 x ( 8 x 2 − 4 x + 5 ) 3 x ( 8 x 2 − 4 x + 5 )

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

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

−2 ( x + 2 ) −2 ( x + 2 )

−2 x ( x 2 − 9 x + 4 ) −2 x ( x 2 − 9 x + 4 )

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

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

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

( b + 5 ) ( a + 3 ) ( b + 5 ) ( a + 3 )

( y + 5 ) ( 8 y + 1 ) ( y + 5 ) ( 8 y + 1 )

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

( u − 1 ) ( u + 6 ) ( u − 1 ) ( u + 6 )

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

( n − 6 ) ( m − 4 ) ( n − 6 ) ( m − 4 )

( x − 7 ) ( 2 x − 5 ) ( x − 7 ) ( 2 x − 5 )

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

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

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

Answers will vary.

Section 6.2 Exercises

( 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 )

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

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

( 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 )

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 )

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

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

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

−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 )

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

( 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 )

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

( x 2 − 7 ) ( x 2 + 4 ) ( x 2 − 7 ) ( x 2 + 4 )

( 3 y − 4 ) ( 3 y − 1 ) ( 3 y − 4 ) ( 3 y − 1 )

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

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

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

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

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

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

( x − 9 ) ( x + 6 ) ( x − 9 ) ( x + 6 )

Section 6.3 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

( 10 y − 1 ) 2 ( 10 y − 1 ) 2

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

3 u 2 ( 5 u − v ) 2 3 u 2 ( 5 u − v ) 2

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

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

6 p 2 ( q − 3 ) ( q + 3 ) 6 p 2 ( q − 3 ) ( q + 3 )

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

( 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 )

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

2 b 2 ( 3 a − 2 ) ( 3 a + 2 ) ( 9 a 2 + 4 ) 2 b 2 ( 3 a − 2 ) ( 3 a + 2 ) ( 9 a 2 + 4 )

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

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

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

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

( 6 a + 5 b ) ( 36 a 2 − 30 a b + 25 b 2 ) ( 6 a + 5 b ) ( 36 a 2 − 30 a b + 25 b 2 )

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

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

9 ( x + 1 ) ( x 2 + 3 ) 9 ( x + 1 ) ( x 2 + 3 )

− ( 3 y + 5 ) ( 21 y 2 − 30 y + 25 ) − ( 3 y + 5 ) ( 21 y 2 − 30 y + 25 )

( 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

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

( 3 x + 1 ) ( 3 x 2 + 1 ) ( 3 x + 1 ) ( 3 x 2 + 1 )

Section 6.4 Exercises

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

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

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

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

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

4 u 2 ( u + 1 ) ( u 2 − u + 1 ) 4 u 2 ( u + 1 ) ( u 2 − u + 1 )

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

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

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

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

( 3 x - 2 ) 2 ( 3 x - 2 ) 2

Section 6.5 Exercises

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

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

x = 1 / 2 x = 1 / 2

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 = −9 / 4 , y = 9 / 4 y = −9 / 4 , y = 9 / 4

n = −6 / 11 , n = 6 / 11 n = −6 / 11 , n = 6 / 11

x = 2 , x = −5 x = 2 , x = −5

x = 3 / 2 , x = −1 x = 3 / 2 , x = −1

x = 2 , x = −4 / 3 x = 2 , x = −4 / 3

x = 3 / 2 x = 3 / 2

x = −3 / 2 , x = 1 / 3 x = −3 / 2 , x = 1 / 3

p = 0 , p = ¾ p = 0 , p = ¾

x = 0 , x = 6 x = 0 , x = 6

x = 0 , x = –1 / 3 x = 0 , x = –1 / 3

ⓐ x = 2 x = 2 or x = 6 x = 6 ⓑ ( 2 , −4 ) ( 2 , −4 ) ( 6 , −4 ) ( 6 , −4 )

ⓐ x = 3 2 x = 3 2 or x = 3 4 x = 3 4 ⓑ ( 3 2 , −4 ) ( 3 2 , −4 ) ( 3 4 , −4 ) ( 3 4 , −4 )

ⓐ x = 2 3 x = 2 3 or x = − 2 3 x = − 2 3 ⓑ ( 2 3 , 0 ) ( 2 3 , 0 ) , ( − 2 3 , 0 ) ( − 2 3 , 0 ) ⓒ ( 0 , −4 ) ( 0 , −4 )

ⓐ x = 5 3 x = 5 3 or x = − 1 2 x = − 1 2 ⓑ ( 5 3 , 0 ) ( 5 3 , 0 ) , ( − 1 2 , 0 ) ( − 1 2 , 0 ) ⓒ ( 0 , −5 ) ( 0 , −5 )

−13 , −11 −13 , −11 and 11, 13

−14 , −12 −14 , −12 and 12, 14

Review Exercises

3 a b 2 3 a b 2

7 ( 5 y + 12 ) 7 ( 5 y + 12 )

3 x ( 6 x 2 − 5 ) 3 x ( 6 x 2 − 5 )

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

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

( 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 )

( a + 3 ) ( a + 11 ) ( a + 3 ) ( a + 11 )

( m + 9 ) ( m − 6 ) ( m + 9 ) ( m − 6 )

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

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

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

( 5 y + 9 ) ( y + 1 ) ( 5 y + 9 ) ( y + 1 )

( 5 y + 1 ) ( 2 y − 11 ) ( 5 y + 1 ) ( 2 y − 11 )

−9 ( 9 a − 1 ) ( a + 2 ) −9 ( 9 a − 1 ) ( a + 2 )

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

( 3 x − 1 ) ( 5 x + 2 ) ( 3 x − 1 ) ( 5 x + 2 )

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

3 ( 2 a − 7 ) ( 3 a + 1 ) 3 ( 2 a − 7 ) ( 3 a + 1 )

( x 2 − 15 ) ( x 2 + 2 ) ( x 2 − 15 ) ( x 2 + 2 )

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

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

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

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

n ( 13 n + 1 ) ( 13 n − 1 ) n ( 13 n + 1 ) ( 13 n − 1 )

( 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

5 u 2 ( u + 3 ) ( u − 3 ) 5 u 2 ( u + 3 ) ( u − 3 )

( b − 4 ) ( b 2 + 4 b + 16 ) ( b − 4 ) ( b 2 + 4 b + 16 )

( 2 b + 5 c ) ( b − c ) ( 2 b + 5 c ) ( b − c )

5 ( q + 3 ) ( q − 6 ) 5 ( q + 3 ) ( q − 6 )

( 4 x − 3 y + 8 ) ( 4 x − 3 y − 8 ) ( 4 x − 3 y + 8 ) ( 4 x − 3 y − 8 )

b = −1 / 5 , b = −1 / 6 b = −1 / 5 , b = −1 / 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

ⓐ x = −7 x = −7 or x = −4 x = −4 ⓑ ( −7 , −8 ) ( −7 , −8 ) ( −4 , −8 ) ( −4 , −8 )

ⓐ x = 7 8 x = 7 8 or x = − 7 8 x = − 7 8 ⓑ ( 7 8 , 0 ) , ( 7 8 , 0 ) , ( − 7 8 , 0 ) ( − 7 8 , 0 ) ⓒ ( 0 , −49 ) ( 0 , −49 )

The numbers are −21 −21 and −19 −19 or 19 and 21.

The lengths are 8, 15, and 17 ft.

Practice Test

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

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

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

( 3 s − 2 ) 2 ( 3 s − 2 ) 2

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

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

a = 4 / 5 , a = −6 a = 4 / 5 , a = −6

The width is 12 inches and the length is 14 inches.

ⓐ x = 3 x = 3 or x = 4 x = 4 ⓑ ( 3 , −7 ) ( 3 , −7 ) ( 4 , −7 ) ( 4 , −7 )

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Access for free at https://openstax.org/books/intermediate-algebra/pages/1-introduction

• Authors: Lynn Marecek
• Publisher/website: OpenStax
• Book title: Intermediate Algebra
• Publication date: Mar 14, 2017
• Location: Houston, Texas
• Book URL: https://openstax.org/books/intermediate-algebra/pages/1-introduction
• Section URL: https://openstax.org/books/intermediate-algebra/pages/chapter-6

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Eureka Math Grade 6 Module 4 Lesson 6 Answer Key

Engage ny eureka math 6th grade module 4 lesson 6 answer key, eureka math grade 6 module 4 lesson 6 example answer key.

Example 1. Expressions with Only Addition, Subtraction, Multiplication, and Division

What operations are evaluated first? Answer: Multiplication and division are evaluated first, from left to right.

What operations are always evaluated last? Answer: Addition and subtraction are always evaluated last, from left to right.

Example 2. Expressions with Four Operations and Exponents 4 + 9 2 ÷ 3 × 2 – 2

What operation is evaluated first? Answer: Exponents (9 2 = 9 × 9 = 81)

What operations are evaluated next? Answer: Multiplication and division, from left to right (81 ÷ 3 = 27; 27 × 2 = 54)

What operations are always evaluated last? Answer: Addition and subtraction, from left to right (4 + 54 = 58; 58 – 2 = 56)

What is the final answer? Answer: 56

Example 3. Expressions with Parentheses Consider a family of 4 that goes to a soccer game. Tickets are $5.00 each. The mom also buys a soft drink for $2.00. How would you write this expression? Answer: 4 × 5 + 2

How much will this outing cost? Answer: $22

Consider a different scenario: The same family goes to the game as before, but each of the family members wants a drink. How would you write this expression? Answer: 4 × (5 + 2)

Why would you add the 5 and 2 first? Answer: We need to determine how much each person spends. Each person spends $7; then, we multiply by 4 people to figure out the total cost.

How much will this outing cost? Answer: $28

How many groups are there? Answer: 4

What does each group comprise? Answer: $5 + $2, or $7

Example 4. Expressions with Parentheses and Exponents 2 × (3 + 4) 2 Which value will we evaluate first within the parentheses? Evaluate. Answer: First, evaluate 4 2 which is 16; then, add 3.The value of the parentheses is 19. 2 × (3 + 4 2 ) 2 × (3 + 16) 2 × 19

Evaluate the rest of the expression. Answer: 2 × 19 = 38

What do you think will happen when the exponent in this expression is outside of the parentheses? 2 × (3 + 4) 2

Will the answer be the same? Answer: Answers will vary.

Which should we evaluate first? Evaluate. Answer: Parentheses 2 × (3 + 4) 2 2 × (7) 2

What happened differently here than in our last example? Answer: The 4 was not raised to the second power because it did not have an exponent. We simply added the values inside the parentheses.

What should our next step be?

We need to evaluate the exponent next. Answer: 7 2 = 7 × 7 = 49

Evaluate to find the final answer. Answer: 2 × 49 98

What do you notice about the two answers? Answer: The final answers were not the same.

What was different between the two expressions? Answer: Answers may vary. In the first problem, a value inside the parentheses had an exponent, and that value was evaluated first because it was inside of the parentheses. In the second problem, the exponent was outside of the parentheses, which made us evaluate what was in the parentheses first; then, we raised that value to the power of the exponent.

What conclusions can you draw about evaluating expressions with parentheses and exponents? Answer: Answers may vary. Regardless of the location of the exponent in the expression, evaluate the parentheses first. Sometimes there will be values with exponents inside the parentheses. If the exponent is outside the parentheses, evaluate the parentheses first, and then evaluate to the power of the exponent.

Eureka Math Grade 6 Module 4 Lesson 6 Exercise Answer Key

Exercise 1. 4 + 2 × 7 Answer: 4 + 14 18

Exercise 2. 36 ÷ 3 × 4 Answer: 12 × 4 48

Exercise 3. 20 − 5 × 2 Answer: 20 − 10 10

Exercise 4. 90 − 5 2 × 3 Answer: 90 − 25 × 3 90 − 75 15

Exercise 5. 4 3 + 2 × 8 Answer: 64 + 2 × 8 64 + 16 80

Exercise 6. 2 + (9 2 ) Answer: 2 + (81 – 4) 2 + 77 79

Exercise 7. 2 . (13 + 5 – 14 ÷ (3 + 4) Answer: 2 . (13 + 5 – 14 ÷ 7) 2 . (13 + 5 – 2) 2 . 16 32

Exercise 8. 7 + (12 – 3 2 ) Answer: 7 + (12 – 9) 7 + 3 10

Exercise 9. 7 + (12 – 3) 2 Answer: 7 + 9 2 7 + 81 88

Eureka Math Grade 6 Module 4 Lesson 6 Problem Set Answer Key

Evaluate each expression.

Question 1. 3 × 5 + 2 × 8 + 2 Answer: 15 + 16 + 2 33

Question 2. ($1.75 + 2 × $0.25 + 5 × $0.05) × 24 Answer: ($1.75 + $0.50 + $0.25) × 24 $2.50 × 24 $60.00

Question 3. (2 × 6) + (8 × 4) + 1 Answer: 12 + 32 + 1 45

Question 4. ((8 × 1.95) + (3 × 2.95) + 10.95) × 1.06 Answer: (15.6 + 8.85 + 10.99) × 1.06 35.4 × 1.06 37.54

Question 5. ((12 ÷ 3) 2 – (18 ÷ 3 2 )) × (4 ÷ 2) Answer: (4 2 − (18 ÷ 9)) × (4 ÷ 2) (16 – 2) × 2 14 × 2 28

Eureka Math Grade 6 Module 4 Lesson 6 Exit Ticket Answer Key

Question 1. Evaluate this expression: 39 ÷ (2 + 1) – 2 × (4 + 1). Answer: 39 ÷ 3 − 2 × 5 13 − 10 3

Question 2. Evaluate this expression: 12 × (3 + 2 2 ÷ 2 − 10 Answer: 12 × (3 + 4) ÷2 − 10 12 × 7 ÷ 2 − 10 84 ÷ 2 − 10 42 − 10 32

Question 3. Evaluate this expression: 12 × (3 + 2) 2 ÷ 2 – 10. Answer: 12 × 5 2 ÷ 2 – 10 12 × 25 ÷ 2 − 10 300 ÷ 2 − 10 150 − 10 140

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