How do you multiply #(2x - 1) ( x ^ { 2} + 2x + 4)#?

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Answer 1 · 2018-02-23T23:44:03

#2x^3+3x^2+6x-4#

We need to multiply each term in the binomial #(2x-1)# by #(x^2+2x+4)# individually and add the resulting expressions together.

The terms in the binomial are: #2x, -1#

First, let's calculate

#(2x)(x^2+2x+4)#:

#(2x)(x^2+2x+4)=(2x)(x^2)+(2x)(2x)+(4)(2x)=2x^3+4x^2+8x#

Now, let's calculate:

#(-1)(x^2+2x+4)#:

#(-1)(x^2+2x+4)=-(x^2+2x+4)=-x^2-2x-4#

Add these two expressions together:

#2x^3+4x^2+8x+(-x^2-2x-4)=2x^3+4x^2+8x-x^2-2x-4#

#2x^3+4x^2+8x-x^2-2x-4=2x^3+3x^2+6x-4#

Answer 2 · 2018-02-24T01:41:06

#=2x^3+3x^2+6x-4#

#(2x-1)(x^2+2x+4)#

Use the distributive property

#(2x)(x^2)+(2x)(2x)+(2x)(4)+(-1)(x^2)+(-1)(2x)+(-1)(4)#

#=2x^3+4x^2+8x-x^2-2x-4#

#=2x^3+3x^2+6x-4#