Question

factorise this math fastly​

Answer 1

let x-y=a

4a^2-12a+9=0

4a^2-6a-6a+9=0

2a(2a-3)-3(2a-3)=0

ans:2a-3=0

a=3/2

x-y=3/2

Answer 2

$p(x-y)=4(x-y)^2-12(x-y)+9=0$

$\large \textsc{For making the process simpler, I'm taking x-y as k . }$

$\textit{Taking \ x-y=k ,}\\ \\ \\ \Rightarrow\ 4(x-y)^2-12(x-y)+9 \\ \\ \Rightarrow\ 4k^2-12k+9 \\ \\ \Rightarrow\ 4k^2-6k-6k+9 \\ \\ \Rightarrow\ 2k(2k-3)-3(2k-3) \\ \\ \Rightarrow\ (2k-3)(2k-3) \\ \\ \Rightarrow\ (2k-3)^2 \\ \\ \Rightarrow\ (2(x-y)-3)^2 \\ \\ \Rightarrow\ (2x-2y-3)^2 \\ \\ \\ \therefore\ 4(x-y)^2-12(x-y)+9=\bold{(2x-2y-3)^2}$

$\boxed{\mathbb{HENCE\ FACTORIZED!!!}}$