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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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