Mathematics
Factorise :
25(2x - y)2 - 16(x - 2y)2
Factorisation
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Answer
25(2x - y)2 - 16(x - 2y)2
Using the formula
[∵ (x2 - y2) = (x + y)(x - y)]
= (5(2x - y))2 - (4(x - 2y))2
= (5(2x - y) + 4(x - 2y))(5(2x - y) - 4(x - 2y))
= (10x - 5y + 4x - 8y)(10x - 5y - 4x + 8y)
= (10x + 4x - 5y - 8y)(10x - 4x - 5y + 8y)
= (14x - 13y)(6x + 3y)
= (14x - 13y)3(2x + y)
Hence,25(2x - y)2 - 16(x - 2y)2 = 3(14x - 13y)(2x + y)
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