1
Question
Factorize:
xy9−yx9
Factorize:
xy9−yx9
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Solution
xy9−yx9=xy(y8−x8)=−xy(x8−y8)=−xy[(x4)2−(y4)2]=−xy(x4+y4)(x4−y4){∵a2−b2=(a+b)(a−b)}=−xy(x4+y4){(x2)2−(y2)2}=−xy(x4+y4)(x2+y2)(x2−y2)=−xy(x4+y4)(x2+y2)(x+y)(x−y)=−xy(x−y)(x+y)(x2+y2)(x4+y4)
xy9−yx9=xy(y8−x8)=−xy(x8−y8)=−xy[(x4)2−(y4)2]=−xy(x4+y4)(x4−y4){∵a2−b2=(a+b)(a−b)}=−xy(x4+y4){(x2)2−(y2)2}=−xy(x4+y4)(x2+y2)(x2−y2)=−xy(x4+y4)(x2+y2)(x+y)(x−y)=−xy(x−y)(x+y)(x2+y2)(x4+y4)
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