Distributive Property

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a(b + c) = ab + ac

Parentheses can be removed by multiplying the outside factor to each term inside the parentheses.

Example:  5(3x + 8)

= 5(3x) + 5(8)

= 15x + 40

 

Note: A negative sign outside parentheses can be understood as the coefficient -1. The distributive property may then be applied to remove the parentheses.

Example:  −(4x + 3)

= −1(4x + 3)

= −4x − 3

 

Recall also that subtracting a number is the same as adding its opposite.

Examples:  7 − 4

= 7 + (−4) = 3

6 − (−2)

= 6 + 2 = 8

 

 

 

Practice

1.  Rewrite each subtraction expression below as adding its opposite.

a)  6 − 3

b)  −x − 4

c)  −5p − 25

 

2.  Use the distributive property to remove parentheses.

a)  3(x − 3)

b)  −2(4a + 3)

c)  −(5x − 2)

d)  2x(x + 3)

e)  2(x + y − 3)

f)  −(5x − y + 2)