Question
Factor polynomial $$ 20c^{2}-45d^{2} $$
Answer
$$ 20c^{2}-45d^{2} = 5(2c+3d)(2c-3d) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ 5 } $:
$$ 20c^2-45d^2 = 5 ( 4c^2-9d^2 ) $$Step 2 :
Rewrite $ 4c^2-9d^2 $ as:
$$ \color{blue}{ 4c^2-9d^2 = (2c)^2 - (3d)^2 } $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = 2c $ and $ II = 3d $ , we have:
$$ 4c^2-9d^2 = (2c)^2 - (3d)^2 = ( 2c-3d ) ( 2c+3d ) $$This page was created using
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