Mathematics
Factorise :
25(2x + y)2 - 16(x - y)2
Factorisation
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Answer
25(2x + y)2 - 16(x - y)2
= (5(2x + y))2 - (4(x - y))2
= (10x + 5y)2 - (4x - 4y)2
Using the formula
[∵ (x2 - y2) = (x + y)(x - y)]
= ((10x + 5y) + (4x - 4y))((10x + 5y) - (4x - 4y))
= (10x + 5y + 4x - 4y)(10x + 5y - 4x + 4y)
= (10x + 4x + 5y - 4y)(10x - 4x + 5y + 4y)
= (14x + y)(6x + 9y)
= (14x + y)3(2x + 3y)
Hence,25(2x + y)2 - 16(x - y)2 = 3(14x + y)(2x + 3y)
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