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Mathematics

Factorise :

2(x + 2y)2 - 5(x + 2y) + 2

Factorisation

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Answer

2(x + 2y)2 - 5(x + 2y) + 2

= 2(x + 2y)2 - (4 + 1)(x + 2y) + 2

= 2(x + 2y)2 - 4(x + 2y) - 1(x + 2y) + 2

= [2(x + 2y)2 - 4(x + 2y)] - [1(x + 2y) - 2]

= 2(x + 2y)[(x + 2y) - 2] - 1[(x + 2y) - 2]

= [(x + 2y) - 2][2(x + 2y) - 1]

= [x + 2y - 2][2x + 4y - 1]

Hence,2(x + 2y)2 - 5(x + 2y) + 2 = [x + 2y - 2][2x + 4y - 1]

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