Question

factorise: 4(x-y)^2-12(x-y)+9​

Answer 1

Step-by-step explanation:

Given  4(x - y)2-12(x - y) + 9

⇒  4( x - y)2- 6( x - y ) - 6(x - y)  + 9

⇒ 2( x -y) [ 2( x -y) - 3] - 3[ 2( x -y) - 3].

⇒ [ 2( x -y) - 3][ 2( x -y) - 3]

⇒ (2x - 2y - 3)2 .

Answer 2

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).