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Mathematics

Factorise :

(2a + b)2 + 5(2a + b) + 6

Factorisation

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Answer

(2a + b)2 + 5(2a + b) + 6

= (2a + b)2 + (2 + 3)(2a + b) + 6

= (2a + b)2 + 2(2a + b) + 3(2a + b) + 6

= [(2a + b)2 + 2(2a + b)] + [3(2a + b) + 6]

= (2a + b)[(2a + b) + 2] + 3[(2a + b) + 2]

= [(2a + b) + 2][(2a + b) + 3]

= [2a + b + 2][2a + b + 3]

Hence,(2a + b)2 + 5(2a + b) + 6 = (2a + b + 2)(2a + b + 3)

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