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Mathematics

Factorise the following:

4a2 - b2 + 2a + b

Factorisation

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Answer

4a2 - b2 + 2a + b = (2a)2 - b2 + 2a + b.

Using identity,

a2 - b2 = (a - b)(a + b).

(2a)2 - b2 + 2a + b = (2a - b)(2a + b) + (2a + b)

= (2a + b)(2a - b + 1).

Hence, 4a2 - b2 + 2a + b = (2a + b)(2a - b + 1).

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