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Question
Factorize the following expressions:
x4y4 - xy
Solution
= xy (x3 y3 -1)
= xy (( xy )3 -13 )
= xy ( xy -1)(( xy)2 + ( xy )1+12 ) [∵ a3 - b3 = (a - b)(a2 + ab + b2 ) ]
= xy (xy -1)(x2 y2 + xy +1)
∴ x4 y4 - xy = xy ( xy -1)(x2 y2 + xy +1)
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