Factor polynomial $$ 216ax^{4}y-6ay^{5} $$
Answer
$$ 216ax^{4}y-6ay^{5} = 6ay(6x^{2}+y^{2})(6x^{2}-y^{2}) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ 6ay } $:
$$ 216ax^4y-6ay^5 = 6ay ( 36x^4-y^4 ) $$Step 2 :
Rewrite $ 36x^4-y^4 $ as:
$$ \color{blue}{ 36x^4-y^4 = (6x^2)^2 - (y^2)^2 } $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = 6x^2 $ and $ II = y^2 $ , we have:
$$ 36x^4-y^4 = (6x^2)^2 - (y^2)^2 = ( 6x^2-y^2 ) ( 6x^2+y^2 ) $$This page was created using
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