Question
Factor polynomial $$ 32a^{2}-50b^{2} $$
Answer
$$ 32a^{2}-50b^{2} = 2(4a+5b)(4a-5b) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ 2 } $:
$$ 32a^2-50b^2 = 2 ( 16a^2-25b^2 ) $$Step 2 :
Rewrite $ 16a^2-25b^2 $ as:
$$ \color{blue}{ 16a^2-25b^2 = (4a)^2 - (5b)^2 } $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = 4a $ and $ II = 5b $ , we have:
$$ 16a^2-25b^2 = (4a)^2 - (5b)^2 = ( 4a-5b ) ( 4a+5b ) $$This page was created using
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