Factor polynomial $$ 32m^{4}n^{3}+16m^{3}n^{4}+2m^{2}n^{5} $$
Answer
$$ 32m^{4}n^{3}+16m^{3}n^{4}+2m^{2}n^{5} = 2m^{2}n^{3}(4m+n)(4m+n) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ 2m^2n^3 } $:
$$ 32m^4n^3+16m^3n^4+2m^2n^5 = 2m^2n^3 ( 16m^2+8mn+n^2 ) $$Step 2 :
Note that the polynomial $ 16m^2+8mn+n^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 = 4m } $ and $ \color{red}{ B = n } $ so,
$$ 16m^2+8mn+n^2 = ( \color{blue}{ 4m } + \color{red}{ n } )^2 $$This page was created using
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