Question

How do you multiply `(x+4)(3x^2-8x-7)`?

Answer 1

`3x^3 +4x^2-39x-28`

Explanation:

To multiply two polynomials requires distribution. Each term of one polynomial must multiple each of the terms in the other polynomial.

We start with:

`(x+4)(3x^2-8x-7)`

`=x(3x^2-8x-7) + 4(3x^2-8x-7)`

First we multiply `x` from the first polynomial by each term of the second polynomial:

`=3x^3 -8x^2-7x + 4(3x^2-8x-7)`

Now we multiply `4` from the first polynomial by each term of the second polynomial:

`=3x^3 - 8x^2 -7x + 12x^2 -32x-28`

Now we simplify:

`=color(blue)(3x^3) - color(orange)(8x^2) -color(red)(7x) + color(orange)(12x^2) -color(red)(32x)-28`

`=color(blue)(3x^3) +color(orange)(4x^2)-color(red)(39x)-28`

`=> color(green)(3x^3 +4x^2-39x-28)`