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Question
Factorize the following expressions:
x6 + y6
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Solution
x6 + y6
= (x2)3 + ( y2)3
= (x2 + y2 )((x2)2 - x2 y2 + (y2)2) [∵ a3 + b3 = (a + b)(a2 - ab + b2)]
= (x2 + y2 )(x4 - x2 y2 + y4)
∴ x6 + y6 = (x2 + y2 )(x4 - x2 y2 + y4 )
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