Question

How do you multiply `(3x + 2) ( 3x ^ { 2} - x + 1)`?

Answer 1

`(3x+2)(3x^2-x-1)=9x^3+3x^2-5x-2`

Explanation:

Given: `(3x+2)(3x^2-x-1)`

We will start by multiplying `(3x^2-x-1)` by `+2` from the first term:

`(3x^2-x-1)xx (+2) = 6x^2-2x-2`

And then multiply `(3x^2-x-1)` by `3x`from the first term:

`(3x^2-x-1)xx(3x) = 9x^3-3x^2-3x`

Then we can add up everything we obtained (officially called combining like terms):

`(3x+2)(3x^2-x-1)=6x^2-2x-2 + 9x^3-3x^2-3x`

`(3x+2)(3x^2-x-1)=9x^3+6x^2-3x^2-2x-3x-2`

`(3x+2)(3x^2-x-1)=9x^3+3x^2-5x-2`

Always be careful of multiplication by negative numbers when they occur in other similar problems.