Objective- To use the distributive property

to simplify variable expressions. Distributive Propertya(b + c) = ab + ac

Order of Operations Distributive Property

6(3 + 5) 6(3 + 5)6(8)

48

6(3) + 6(5)

18 + 30

48

Why distribute when order of operations is faster ?3(x 2) 3(x) 3(2) 3x 6

Use the distributive property to simplify.

1) 3(x + 7)

2) 2(a + 4)

3) 7(8 + m)

4) 3(4 + a)

5) (3 + k)5

6) x(a + m)

7) 4(3 + r)

8) 2(x + 8)

9) 7(2m + 3y + 4)

10) (6 + 2y + a)3

3x

2a

56

12

15

ax + mx

12 + 4r

2x + 16

14m + 21y + 28

18 + 6y + 3a

+ 21

+ 8

+ 7m

+ 3a

+ 5k

Use the distributive property to simplify.

1) 4(y + 7)

2) 3(b + 6)

3) 5(9 + m)

4) 5(4 + a)

5) (7 + k)6

6) a(c + d)

7) 8(3 + r)

8) 4(x + y + 1)

9) 5(2m + 3 + t)

10) (11 + 2y)+3y

4y + 28

3b + 18

45 + 5m

20 + 5a

42 + 6k

ac + ad

24 + 8r

4x + 4y + 4

10m + 15 + 5t

11 + 5y

Geometric Model for Distributive Property3 7

4

Two ways to find the total area.

Width by total length Sum of smaller rectangles

4(3 + 7)

Geometric Model for Distributive Property3 7

4

Two ways to find the total area.

Width by total length Sum of smaller rectangles

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

4(3) 4(7)

=

Geometric Model for Distributive Property4 x

9

Two ways to find the total area.

Width by total length Sum of smaller rectangles

9(4 + x) 9(4) + 9(x)=

Find the missing factor.

1)

2)

3)

15x (5x)( )

4)

5)

12a (2a)( )

2x (x)( )

36a (9a)( )

27x (3x)( )

3

6

2

4

9

Factoring

GCF - Greatest Common Factor

3

6

7 m

Factoring

Find the GCF of the following mentally.

1)

2)

3)

15x 12

30 42a

14m 21m

4) 16k 40 8

7( )

Factoring

Factor the following expression.

1)

2)

3)

4)

12m 10

14a 7

15x 20y 30

8m 12x 20

2( )6m 5

2a 1

5( )3x 4y 6

4( )2m 3x 5

One type involves the Distributive Property in reverse.

5( )

Factor the following expression.

5)

6)

7)

8)

22k 33

15 35t

24c 12d 18

9b 6 21a

11( )2k 3

3 7t

6( )4c 2d 3

3( )3b 2 7a

Factoring

One type involves the Distributive Property in reverse.

Like terms - variable terms that differ only in their coefficients.

Like Terms Unlike Terms

7x 3x

5y y

10xy 2yx

7x 3y

5y 2y

2a 3ab

2

32a b 6 2ba 25x y 7 2xy

4 2p 2p 4p 2p

Like Terms

Simplify by combining like terms.1) 7x + 4y + 2x + y

2) 3m + 10n + 4m + 1

3) 7x + 3y

4) 6x + (5x) + 2x + 3

5) 4k + (2j) + 6k + j

6) 10 + 4x + 3y + 17x

7)

8)

9x

7m

7x + 3y

13x

10k

21x

+ 5y

+ 10n + 1

+ 3

+ 3j

+ 3y + 102 23y y 6y y

29y 2y2 23 2m 4t m t

7 7 25 m

7 5t

Simplify the expression using the Distributive Property and then combining like terms.

1)

2)

3)

4)

3(a 4) 2a

5x 4(x 7)

2a 6(5 a) a

3(b 4) 2(b 5)

3a 12 2a

5a 12

4x 285x 9x 28

30 6a2a a9a 30

3b 12 2b 10 5b 22

Simplify each variable expression.5) 7(x + 4) + 2x

6) 5x + 3(x + 1)

7) a + 2(4 + a ) + 1

7x + 28 + 2x

9x + 28

5x + 3x + 3

8x + 3

a + 8 + 2a + 1

3a + 9

8) 3(b + 2) + 6b

9) 2(3m + 1) + 4m

10) 3(k + m) + 5(k + 2m)

3b + 6 + 6b

9b + 6

6m + 2 + 4m

10m + 2

3k + 3m

8k + 13m

+ 5k + 10m