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Mathematics

Factorise :

4(2a + b)2 - (a - b)2

Factorisation

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Answer

4(2a + b)2 - (a - b)2

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

= (4a + 2b)2 - (a - b)2

Using the formula

[∵ (x2 - y2) = (x + y)(x - y)]

= ((4a + 2b) + (a - b))((4a + 2b) - (a - b))

= (4a + 2b + a - b)(4a + 2b - a + b)

= (4a + a + 2b - b)(4a - a + 2b + b)

= (5a+ b)(3a+ 3b)

= (5a+ b)3(a+ b)

Hence,4(2a + b)2 - (a - b)2 = 3(5a+ b)(a+ b)

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