Question

4(x - y)^2 - 12(x - y) +9​

Answer 1

Answer:

4 (x - y) ^2 - 12 (x - y) + 9 = [2*(x - y)]^2 - 2*2*3 (x - y) + 3^2

Notice: it has the form [(a^2–2*a*b+b^2 = (a-b)^2] where a = 2*(x - y) and b = 3.

4 (x - y) ^2 - 12 (x - y) + 9 = (2*(x-y) -3)^2 ( Don’t leave this way. Strictly speaking, factorization means to have factors not power)

Therefore, 4 (x - y) ^2 - 12 (x - y) + 9 = (2*(x-y) -3)(2*(x-y) -3).

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Answer 2

Answer:

(2x-2y-3)(2x-2y-3)

Step-by-step explanation:

Lets assume x-y to hold a value "a".

Therefore the equation henceforth becomes :

4a^2 - 12a + 9

we notice it is a perfect square, therefore :

= (2a-3)^2

now let's substitute the value of "a".

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

= [2x-2y-3]^2

= (2x-2y-3)(2x-2y-3)

[EDIT] The answer posted previously to the question is also absolutely correct but this method is useful when given questions like this which are even bigger to avoid confusion. Have a great day!