Question

How do you simplify `(6x + 2)(2x^2 - 6x + 1)`?

Answer 1

See the entire simplification 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)(6x) + color(red)(2))(color(blue)(2x^2) - color(blue)(6x) + color(blue)(3))` becomes:

`(color(red)(6x) xx color(blue)(2x^2)) - (color(red)(6x) xx color(blue)(6x)) + (color(red)(6x) xx color(blue)(1)) + (color(red)(2) xx color(blue)(2x^2)) - (color(red)(2) xx color(blue)(6x)) + (color(red)(2) xx color(blue)(1))`

`12x^3 - 36x^2 + 6x + 4x^2 - 12x + 2`

We can now group and combine like terms:

`12x^3 - 36x^2 + 4x^2 + 6x - 12x + 2`

`12x^3 + (-36 + 4)x^2 + (6 - 12)x + 2`

`12x^3 - 32x^2 - 6x + 2`