Question

Using the distributive property, Marta multiplied the binomial (2x + 3) by the trinomial (x2 + x – 2) and got the expression below.

(2x)(x2) + (2x)(x) + (2x)(–2) + (3)(x2) + (3)(x) + (3)(–2)

Which is the simplified product?

Answer 1

`2x^3 + 5x^2 -x -6`

Explanation:

Given

`(2x)(x^2) + (2x)(x) + (2x)(-2) + (3)(x^2) + (3)(x) + (3)(-2)`

Required

The simplified product

We have:

`(2x)(x^2) + (2x)(x) + (2x)(-2) + (3)(x^2) + (3)(x) + (3)(-2)`

Open bracket

`(2x)(x^2) + (2x)(x) + (2x)(-2) + (3)(x^2) + (3)(x) + (3)(-2) = 2x^3 + 2x^2 -4x + 3x^2 + 3x -6`

Collect like terms

`(2x)(x^2) + (2x)(x) + (2x)(-2) + (3)(x^2) + (3)(x) + (3)(-2) = 2x^3 + 2x^2+ 3x^2 -4x + 3x -6`
`(2x)(x^2) + (2x)(x) + (2x)(-2) + (3)(x^2) + (3)(x) + (3)(-2) = 2x^3 + 5x^2 -x -6`

Hence, the simplified product is:
`2x^3 + 5x^2 -x -6`