2.5: Factoring the GCF
- Page ID
- 13971
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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
\[\begin{array}{rcl lll} 15x+20y&=&3\cdot 5x+4\cdot 5y\\ &=&5(3x+4y) \end{array}\]