Distributive Property and Factoring Linear Expressions

Distributive Property 1

100

2 (x + y)

2x + 2 Y

200

(4 + x ) y

4y + xy

300

5 (x - 7)

5x - 35

400

(12 - y) 8

96-8y

500

x - (y+z)

x - y-z

Distributive Property 2

100

4 (7b + 5c)

28b + 20c

200

8 (2+a)

16+8a

300

a (7+b+c)

7a + ab+ac

400

2 (3x + 4y)

6x + 8y

500

x+(-y-z)

Not possible because x is being added to the group not multiplied 

x+(-y-z)

Factoring 1

100

15a + 20b

5(3a+4b)

200

28e + 21

7(4e+3)

300

18ax-15ay

3a(6x-5y)

400

12s+48bs

12s(1+4b)

500

7bt+21b+35bt

7b(t+3+5t)  or 7b(6t+3)

Factoring 2

100

21a + 18b

3(7a+6b)

200

6f-6

6(f-1)

300

15ab-3a

3a(5b-1)

400

51cu+17cv

17c(3u+v)

500

24ax - 40ay+8a

8a(3x-5y+1)

Combining Like Terms

100

Simplify this expression by combining like terms

2a - xy + 5xy

2a + 4xy

200

Simplify by combing like terms

8ab + ab³ - 2a + 10ab

18ab + ab³ - 2a

300

Simplify by combining like Terms

 5 + 3x² - x²

5 + 2x²

400

Simplify by combing like terms

-5x²y + 6xy² + xy² -18

-5x²y + 8xy² -18

500

Factor and simplify

ax (5 + 3x + 2x)

5ax² + 5ax