Question
Factor polynomial $$ x^{9}-a^{15}y^{12} $$
Answer
$$ x^{9}-a^{15}y^{12} = (x^{3}-a^{5}y^{4})(x^{6}+a^{5}x^{3}y^{4}+a^{10}y^{8}) $$
Explanation
To factor $ x^{9}-a^{15}y^{12} $ we can use difference of cubes formula:
$$ I^3 - II^3 = (I - II) (I^2 + I \cdot II + II^2) $$After putting $ I = x^3 $ and $ II = a^5y^4 $ , we have:
$$ x^{9}-a^{15}y^{12} = ( x^{3}-a^{5}y^{4} ) ( x^{6}+a^{5}x^{3}y^{4}+a^{10}y^{8} ) $$This page was created using
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