Factor polynomial $$ a^{2}x+b^{2}x-a^{2}y-b^{2}y $$

$$ a^{2}x+b^{2}x-a^{2}y-b^{2}y = (x-y)(a^{2}+b^{2}) $$

To factor $ a^2x+b^2x-a^2y-b^2y $ we can use factoring by grouping.

Group $ \color{blue}{ a^2x }$ with $ \color{blue}{ b^2x }$ and $ \color{red}{ -a^2y }$ with $ \color{red}{ -b^2y }$ then factor each group.

$$ \begin{aligned} a^2x+b^2x-a^2y-b^2y &= ( \color{blue}{ a^2x+b^2x } ) + ( \color{red}{ -a^2y-b^2y }) = \\ &= \color{blue}{ x( a^2+b^2 )} \color{red}{ -y( a^2+b^2 ) } = \\ &= (x-y)(a^2+b^2) \end{aligned} $$

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