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

2 Answers
Feb 23, 2018

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

Explanation:

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

Feb 24, 2018

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

Explanation:

(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