Answer:
x^3 +8
Explanation:
A product of polynomials is simplified by making use of the distributive property. In effect, each term of one polynomial is multiplied by every term of the other one. Then like terms of the result are combined. (This is very similar to multi-digit numerical multiplication.)
(2 +x)(4 -2x +x^2)
= 2(4 -2x +x^2) +x(4 -2x +x^2)
= (2)(4) +(2)(-2x) +(2)(x^2) +(x)(4) +(x)(-2x) +(x)(x^2)
= 8 -4x +2x^2 +4x -2x^2 +x^3
= x^3 +(2 -2)x^2 +(-4+4)x + 8
= x^3 +8
_____
Additional comment
The factored form can be recognized as the special product, "sum of cubes."