Question
Factor polynomial $$ 18b^{2}-50c^{2} $$
Answer
$$ 18b^{2}-50c^{2} = 2(3b+5c)(3b-5c) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ 2 } $:
$$ 18b^2-50c^2 = 2 ( 9b^2-25c^2 ) $$Step 2 :
Rewrite $ 9b^2-25c^2 $ as:
$$ \color{blue}{ 9b^2-25c^2 = (3b)^2 - (5c)^2 } $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = 3b $ and $ II = 5c $ , we have:
$$ 9b^2-25c^2 = (3b)^2 - (5c)^2 = ( 3b-5c ) ( 3b+5c ) $$This page was created using
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