Question

factorise : 4(x-y)^2-12(x-y)+9

Answer 1

take (x-y) as a
4a^2-12a+9
4a^2-6a-6a+9
2a (2a-3)-3 (2a-3)
(2a-3)(2a-3)
(2x-2y-3)(2x-2y-3)

Answer 2

Let x-y be s.
Therefore, the expression becomes
$4s^{2} -12s+9$
=$(2s)^{2} - 2*2s*3+(3)^{2}$
=$(2s-3)^{2}$
Substituting s as x-y (as mentioned above) we get:
$[2(x-y)+3]^{2}$
=$(2x-2y+3)^{2}$
Ans:=$(2x-2y+3)^{2}$
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