Question

Simplify the polynomial expression given below.

(2x − 1)(2x2 + 5x + 3) + (3x + 6)

The first step is as follows:

2x(2x2 + 5x + 3) − 1(2x2 + 5x + 3) + (3x + 6)


4x³ + 8x² + 4x + 3

4x³ + 8x² + 14x + 9

2x² + 24x + 6

Answer 1

Your first step is correct. Now multiply and combine like terms:

2x(2x^2 + 5x + 3) − 1(2x^2 + 5x + 3) + (3x + 6)
= (4x^3 + 10x^2 + 6x) + (−2x^2 − 5x − 3) + (3x + 6)
= 4x^3 + (10x^2 − 2x^2) + (6x − 5x + 3x) + (−3 + 6)
= 4x^3 + 8x^2 + 4x + 3.

So the simplified polynomial is 4x^3 + 8x^2 + 4x + 3.