Question
Factor polynomial $$ 75x^{2}-27y^{2} $$
Answer
$$ 75x^{2}-27y^{2} = 3(5x+3y)(5x-3y) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ 3 } $:
$$ 75x^2-27y^2 = 3 ( 25x^2-9y^2 ) $$Step 2 :
Rewrite $ 25x^2-9y^2 $ as:
$$ \color{blue}{ 25x^2-9y^2 = (5x)^2 - (3y)^2 } $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = 5x $ and $ II = 3y $ , we have:
$$ 25x^2-9y^2 = (5x)^2 - (3y)^2 = ( 5x-3y ) ( 5x+3y ) $$This page was created using
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