Question

How do you simplify the product `(2x^2 + 5x - 3)(2x + 1)` and write it in standard form?

Answer 1

See a solution process below:

Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`(color(red)(2x^2) + color(red)(5x) - color(red)(3))(color(blue)(2x) + color(blue)(1))` becomes:

`(color(red)(2x^2) xx color(blue)(2x)) + (color(red)(2x^2) xx color(blue)(1)) + (color(red)(5x) xx color(blue)(2x)) + (color(red)(5x) xx color(blue)(1)) - (color(red)(3) xx color(blue)(2x)) - (color(red)(3) xx color(blue)(1))`

`4x^3 + 2x^2 + 10x^2 + 5x - 6x - 3`

We can now combine like terms:

`4x^3 + (2 + 10)x^2 + (5 - 6)x - 3`

`4x^3 + 12x^2 + (-1)x - 3`

`4x^3 + 12x^2 - 1x - 3`

`4x^3 + 12x^2 - x - 3`