Mathematics
Factorise the following:
x9 + y9
Factorisation
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Answer
x9 + y9 = (x3)3 + (y3)3
We know that,
a3 + b3 = (a + b)(a2 - ab + b2)
(x3)3 + (y3)3 = (x3 + y3)[(x3)2 - x3y3 + (y3)2]
= (x3 + y3)(x6 - x3y3 + y6)
= (x + y)(x2 - xy + y2)(x6 - x3y3 + y6)
Hence, x9 + y9 = (x + y)(x2 - xy + y2)(x6 - x3y3 + y6).
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