Mathematics
Factorise the following:
a6 - b6
Factorisation
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Answer
a6 - b6 = (a2)3 - (b2)3.
We know that,
a3 - b3 = (a - b)(a2 + ab + b2).
∴ (a2)3 - (b2)3 = (a2 - b2)[(a2)2 + a2b2 + (b2)2]
= (a2 - b2)(a4 + a2b2 + b4)
= (a - b)(a + b)(a4 + a2b2 + b4)
= (a - b)(a + b)[(a2)2 + 2a2b2 + (b2)2 - a2b2]
=(a - b)(a + b)[(a2 + b2)2 - a2b2]
= (a - b)(a + b)(a2 + b2 + ab)(a2 + b2 - ab)
Hence, a6 - b6 = (a - b)(a + b)(a2 + b2 + ab)(a2 + b2 - ab).
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