Question
Factor polynomial $$ 32a^{2}+48ab+18b^{2} $$
Answer
$$ 32a^{2}+48ab+18b^{2} = 2(4a+3b)(4a+3b) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ 2 } $:
$$ 32a^2+48ab+18b^2 = 2 ( 16a^2+24ab+9b^2 ) $$Step 2 :
Note that the polynomial $ 16a^2+24ab+9b^2 $ is a perfect square trinomial, so we will use the following formula.
$$ A^2 + 2AB + B^2 = (A + B)^2 $$In this example we have $ \color{blue}{ A = 4a } $ and $ \color{red}{ B = 3b } $ so,
$$ 16a^2+24ab+9b^2 = ( \color{blue}{ 4a } + \color{red}{ 3b } )^2 $$This page was created using
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