f(x) = (x + 1)^2 and g(x) = 2(x - 1) Show that gf(x) = 2x(x + 2)

For this question, as we are looking for gf(x) so we first need to plug in our formula for f(x) into the g(x) formula, giving us:
2((x+1)^2 - 1)
We can then expand our squared bracket to get:
2(x^2 + 2x + 1 - 1)
We can see the +1 and -1 term now cancel out leaving us with:
2(x^2 + 2x)
And finally we take the common term from within the bracket to the outside (both terms share an x) to finish with:
2x(x + 2)