Mathematics
Factorise the following:
a4 + b4 - 7a2b2.
Factorisation
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Answer
Above terms can be written as,
a4 + b4 + 2a2b2 - 9a2b2
= [(a2)2 + (b2)2 + 2(a2b2)] - (3ab)2
We know that,
(a + b)2 = a2 + 2ab + b2
and
a2 - b2 = (a - b)(a + b)
∴ [(a2)2 + (b2)2 + 2(a2b2)] - (3ab)2 = (a2 + b2)2 - (3ab)2
= (a2 + b2 + 3ab)(a2 + b2 - 3ab)
Hence, a4 + b4 - 7a2b2 = (a2 + b2 + 3ab)(a2 + b2 - 3ab).
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