Question
Factor polynomial $$ 4x^{2}+xy^{2}+8xy+2y^{3} $$
Answer
$$ 4x^{2}+xy^{2}+8xy+2y^{3} = (x+2y)(4x+y^{2}) $$
Explanation
To factor $ 4x^2+xy^2+8xy+2y^3 $ we can use factoring by grouping.
Group $ \color{blue}{ 4x^2 }$ with $ \color{blue}{ xy^2 }$ and $ \color{red}{ 8xy }$ with $ \color{red}{ 2y^3 }$ then factor each group.
$$ \begin{aligned} 4x^2+xy^2+8xy+2y^3 &= ( \color{blue}{ 4x^2+xy^2 } ) + ( \color{red}{ 8xy+2y^3 }) = \\ &= \color{blue}{ x( 4x+y^2 )} + \color{red}{ 2y( 4x+y^2 ) } = \\ &= (x+2y)(4x+y^2) \end{aligned} $$This page was created using
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