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Mathematics

Factorise :

16(5x + 4)2 - 9(3x - 2)2

Factorisation

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Answer

16(5x + 4)2 - 9(3x - 2)2

Using the formula

[∵ (x2 - y2) = (x + y)(x - y)]

= (4(5x + 4))2 - (3(3x - 2))2

= (4(5x + 4) + 3(3x - 2))(4(5x + 4) - 3(3x - 2))

= (20x + 16 + 9x - 6)(20x + 16 - 9x + 6)

= (20x + 9x + 16 - 6)(20x - 9x + 16 + 6)

= (29x + 10)(11x + 22y)

= (29x + 10)11(x + 2y)

Hence,16(5x + 4)2 - 9(3x - 2)2 = 11(29x + 10)(x + 2y)

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