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Question
Factorize each of the following expression:
xy9 − yx9
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Solution
\[x y^9 - y x^9 \]
\[ = xy( y^8 - x^8 )\]
\[ = xy[( y^4 )^2 - ( x^4 )^2 ]\]
\[ = xy( y^4 + x^4 )( y^4 - x^4 )\]
\[ = xy( y^4 + x^4 )[( y^2 )^2 - ( x^2 )^2 ]\]
\[ = xy( y^4 + x^4 )( y^2 + x^2 )( y^2 - x^2 )\]
\[ = xy( y^4 + x^4 )( y^2 + x^2 )(y + x)(y - x)\]
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