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