Question
Factor polynomial $$ x^{3}+2x^{2}y-2x^{2}-4xy $$
Answer
$$ x^{3}+2x^{2}y-2x^{2}-4xy = x(x-2)(x+2y) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ x } $:
$$ x^3+2x^2y-2x^2-4xy = x ( x^2+2xy-2x-4y ) $$Step 2 :
To factor $ x^2+2xy-2x-4y $ we can use factoring by grouping.
Group $ \color{blue}{ x^2 }$ with $ \color{blue}{ 2xy }$ and $ \color{red}{ -2x }$ with $ \color{red}{ -4y }$ then factor each group.
$$ \begin{aligned} x^2+2xy-2x-4y &= ( \color{blue}{ x^2+2xy } ) + ( \color{red}{ -2x-4y }) = \\ &= \color{blue}{ x( x+2y )} \color{red}{ -2( x+2y ) } = \\ &= (x-2)(x+2y) \end{aligned} $$This page was created using
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