Question

4(x - y)2 – 12(x - y) +9​

Answer 1

Let (x-y) = m, so

4(x-y)^2–12(x-y) + 9 is

4m^2–12m+9 …(1)

Now 4*9 = 36. And -12 = -6–6, so (1) becomes

4m^2–6m-6m+9

= 2m(2m-3) - 3(2m-3)

= (2m-3)(2m-3)

= [2(x-y)-3]^2.

Hence, 4(x-y)^2–12(x-y) + 9 = [2(x-y)-3]^2.

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