Factor polynomial $$ 7x^{4}-28y^{4} $$
Answer
$$ 7x^{4}-28y^{4} = 7(x^{2}+2y^{2})(x^{2}-2y^{2}) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ 7 } $:
$$ 7x^4-28y^4 = 7 ( x^4-4y^4 ) $$Step 2 :
Rewrite $ x^4-4y^4 $ as:
$$ \color{blue}{ x^4-4y^4 = (x^2)^2 - (2y^2)^2 } $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = x^2 $ and $ II = 2y^2 $ , we have:
$$ x^4-4y^4 = (x^2)^2 - (2y^2)^2 = ( x^2-2y^2 ) ( x^2+2y^2 ) $$This page was created using
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