Factor polynomial $$ 45r^{2}-120rs+80s^{2} $$
Answer
$$ 45r^{2}-120rs+80s^{2} = 5(3r-4s)(3r-4s) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ 5 } $:
$$ 45r^2-120rs+80s^2 = 5 ( 9r^2-24rs+16s^2 ) $$Step 2 :
Note that the polynomial $ 9r^2-24rs+16s^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 = 3r } $ and $ \color{red}{ B = 4s } $ so,
$$ 9r^2-24rs+16s^2 = ( \color{blue}{ 3r } - \color{red}{ 4s } )^2 $$This page was created using
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