Question
Factor polynomial $$ x^{14}-16a^{2}b^{2} $$
Answer
$$ x^{14}-16a^{2}b^{2} = (x^{7}+4ab)(x^{7}-4ab) $$
Explanation
Rewrite $ x^14-16a^2b^2 $ as:
$$ \color{blue}{ x^14-16a^2b^2 = (x^7)^2 - (4ab)^2 } $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = x^7 $ and $ II = 4ab $ , we have:
$$ x^14-16a^2b^2 = (x^7)^2 - (4ab)^2 = ( x^7-4ab ) ( x^7+4ab ) $$This page was created using
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