Question

How do you simplify the product `(3x + 1)(4x^2 - 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)(3x) + color(red)(1))(color(blue)(4x^2) - color(blue)(2x) + color(blue)(1))` becomes:

`(color(red)(3x) xx color(blue)(4x^2)) - (color(red)(3x) xx color(blue)(2x)) + (color(red)(3x) xx color(blue)(1)) + (color(red)(1) xx color(blue)(4x^2)) - (color(red)(1) xx color(blue)(2x)) + (color(red)(1) xx color(blue)(1))`

`12x^3 - 6x^2 + 3x + 4x^2 - 2x + 1`

We can now group and combine like terms:

`12x^3 - 6x^2 + 4x^2 + 3x - 2x + 1`

`12x^3 + (-6 + 4)x^2 + (3 - 2)x + 1`

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

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