Factor polynomial $$ 25x^{4}-20x^{3}y^{2}+4x^{2}y^{4} $$
Answer
$$ 25x^{4}-20x^{3}y^{2}+4x^{2}y^{4} = x^{2}(5x-2y^{2})(5x-2y^{2}) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ x^2 } $:
$$ 25x^4-20x^3y^2+4x^2y^4 = x^2 ( 25x^2-20xy^2+4y^4 ) $$Step 2 :
Note that the polynomial $ 25x^2-20xy^2+4y^4 $ is a perfect square trinomial, so we will use the following formula.
$$ A^2 - 2AB + B^2 = (A - B)^2 $$In this example we have $ \color{blue}{ A = 5x } $ and $ \color{red}{ B = 2y^2 } $ so,
$$ 25x^2-20xy^2+4y^4 = ( \color{blue}{ 5x } - \color{red}{ 2y^2 } )^2 $$This page was created using
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