Question

Explain how to simplify x(2x + 3x2). You may indicate an exponent in your answer with ^. For example, 3x2 as 3x^2.

Answer 1

hi, I know I should use the distributive property but am confused on how

Answer 2

btw, the problem is x_2x+3x^2)

Answer 3

\[x(2x+3x ^{2})\] So using the distributive law you get this:\[(2)(x)(x) + (3)(x ^{2})(x)\]Since it doesn't matter in what order you multiply, let's start by multiplying the x's in the first term. So we have this:\[(x ^{1})(x ^{1})= x ^{1+1}\]What equals this:\[x ^{1+1}= x ^{2}\] Now we need to multiply by 2.\[(2)(x ^{2})=2x ^{2}\]Now we need to find out what this is:\[(3)(x ^{2})(x)\]Again start with the x's. So we have this:\[(x ^{2})(x ^{1})=x ^{2+1}\]Which equals this:\[x ^{2+1}=x ^{3}\]Now we need to multiply by 3.\[(3)(x ^{3})=3x ^{3}\]So our answer will be this:\[2x ^{2}+3x ^{3}\]