Mathematics
Factorise the following:
a4 - b4 + 2b2 - 1
Factorisation
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Answer
a4 - b4 + 2b2 - 1
Above terms can be written as,
a4 - (b4 - 2b2 + 1)
= a4 - [(b2)2 - (2 × b2 × 1) + 12]
We know that,
(a - b)2 = a2 - 2ab + b2.
a4 - [(b2)2 - (2 × b2 × 1) + 12] = (a2)2 - (b2 - 1)2.
Using identity,
a2 - b2 = (a - b)(a + b).
(a2)2 - (b2 - 1)2 = (a2 + b2 - 1)(a2 - b2 + 1).
Hence, a4 - b4 + 2b2 - 1 = (a2 + b2 - 1)(a2 - b2 + 1).
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