Factor polynomial $$ 16x^{2}-100y^{2} $$
Answer
$$ 16x^{2}-100y^{2} = 4(2x+5y)(2x-5y) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ 4 } $:
$$ 16x^2-100y^2 = 4 ( 4x^2-25y^2 ) $$Step 2 :
Rewrite $ 4x^2-25y^2 $ as:
$$ \color{blue}{ 4x^2-25y^2 = (2x)^2 - (5y)^2 } $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = 2x $ and $ II = 5y $ , we have:
$$ 4x^2-25y^2 = (2x)^2 - (5y)^2 = ( 2x-5y ) ( 2x+5y ) $$This page was created using
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