
# 2.5: Factoring the GCF


The distributive property of multiplication over addition/subtraction can be reversed.

$$a(b\pm c)=ab\pm ac$$ (right side equals left side) implies $$ab\pm ac=a(b\pm c)$$ (left side equals right side).

Factoring is the art of taking a sum (addition of terms) or difference (subtraction of terms) into a product (multiplication of factors).

Example $$\PageIndex{1}$$

Factor $$15x+20y$$.

Solution

$\begin{array}{rcl lll} 15x+20y&=&3\cdot 5x+4\cdot 5y\\ &=&5(3x+4y) \end{array}$