Exercise 25 Page 593

When using the Distributive Property, we multiply a factor that is outside of the parentheses with all the terms inside of the parentheses.

a (b + c) = a \cdot b + a \cdot c

Therefore, if using the Distributive Property resulted in

6 m - 12,

we must find a factor that

6 m

and

- 12

both share. By breaking down each term into prime factors, we can identify which factors they both share.

2 \cdot 3 \cdot m 6 m - 2 \cdot 3 \cdot 2 12

Assuming that the factor outside of the parentheses is an integer, we have three possibilities.

6 m - 12 6 m - 12 6 m - 12 = 2 (3 m - 6) = 3 (2 m - 4) = 6 (m - 2)