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

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Answer 1 · 2018-03-18T00:44:14

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

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)#