Question
Factor polynomial $$ x^{10}+y^{10} $$
Answer
$$ x^{10}+y^{10} = (x^{2}+y^{2})(x^{8}-x^{6}y^{2}+x^{4}y^{4}-x^{2}y^{6}+y^{8}) $$
Explanation
To factor $ x^{10}+y^{10} $ we can use formula:
$$ I^5 + II^5 = (I + II) (I^4 - I^3 \cdot II + I^2 \cdot II^2 - I \cdot II^3 +II^4) $$After putting $ I = x^2 $ and $ II = y^2 $ , we have:
$$ x^{10}+y^{10} = ( x^{2}+y^{2} ) ( x^{8}-x^{6}y^{2}+x^{4}y^{4}-x^{2}y^{6}+y^{8} ) $$This page was created using
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