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Mathematics LibreTexts

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

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