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