((x+1)-1)^3+2(x+1)^2

Question

composite function

Answer 1

((x+1)-1)^3+2(x+1)^2

Since this is about composite function, you can write

f(x) = (x-1)^3 + 2x^2 and g(x) = x+1

f(g(x)) = ((x+1)-1)^3+2(x+1)^2

Answer 2

((x + 1) - 1)³ + 2(x + 1)²            Given

(x + 1 - 1)³ + 2(x + 1)²               Associative property of addition

(x)³ + 2(x + 1)²                          Simplify

x³ + 2(x + 1)(x + 1)                    Definition of square of a binomial

x³ + 2(x² + x + x + 1)                  FOIL the binomial

x³ + 2(x² + 2x + 1)                     Simplify

x³ + 2x² + 4x + 1                       Distribute the 2