Factor polynomial $$ 2rx^{4}-72ry^{4} $$
Answer
$$ 2rx^{4}-72ry^{4} = 2r(x^{2}+6y^{2})(x^{2}-6y^{2}) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ 2r } $:
$$ 2rx^4-72ry^4 = 2r ( x^4-36y^4 ) $$Step 2 :
Rewrite $ x^4-36y^4 $ as:
$$ \color{blue}{ x^4-36y^4 = (x^2)^2 - (6y^2)^2 } $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = x^2 $ and $ II = 6y^2 $ , we have:
$$ x^4-36y^4 = (x^2)^2 - (6y^2)^2 = ( x^2-6y^2 ) ( x^2+6y^2 ) $$This page was created using
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