Question

Can somebody help me to factor this please?

Answer 1

Answer: \bold{ (x-1)^2[g(x-1)^2-y^2]}

Step-by-step explanation:

Remember that (1 - x) and (x - 1) are opposites so if you multiply (1 - x) by (-1), you get (x - 1).

$g(1-x)^4-y^2(x-1)^2\\\\=g[\bold{(-1)}(1-x)]^4-y^2(x-1)^2\bold{(-1)^4}\\\\=g(x-1)^4-y^2(x-1)^2\\\\=g(x-1)^2(x-1)^2-y^2(x-1)^2\\\\=g(x-1)^2\underline{(x-1)^2}-y^2\underline{(x-1)^2}\\\\\text{Since they share a value, it can be factored out}:\\(x-1)^2[g(x-1)^2-y^2]\\\\\text{NOTE: If the "g" wasn't part of the 2nd factor, it could be factored}\\\text{using the difference of squares.}$