Question

It is asking for me to factor this equation (x-2)(x-2)+6(x-2)+9

this is the final answer (x-1)(x-1) how did this answer come to be?

Answer 1

(x-2)(x-2)+6(x-2)+9
so first we distribute
x^2-2x-2x+4+6x-12+9
group like terms
x^2+2x+1
factor
find what 2 numbers add to get 2 and multiply to get 1
the numbers are 1 and 1
(x+1)(x+1)