Question

4 (x-y)^2 - 12 (x-y) +9​

Answer 1

Answer:

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.

Answer 2

Let x-y be s.

Therefore, the expression becomes

4s^{2} -12s+94s2−12s+9

=(2s)^{2} - 2*2s*3+(3)^{2}(2s)2−2∗2s∗3+(3)2

=(2s-3)^{2}(2s−3)2

Substituting s as x-y (as mentioned above) we get:

[2(x-y)+3]^{2}[2(x−y)+3]2

=(2x-2y+3)^{2}(2x−2y+3)2

Ans:=(2x-2y+3)^{2}(2x−2y+3)2