Question

How do you simplify `(x + 1)(x^2 + x + 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)(x) + color(red)(1))(color(blue)(x^2) + color(blue)(x) + color(blue)(1))` becomes:

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

`x^3 + x^2 + x + x^2 + x + 1`

We can now group and combine like terms:

`x^3 + x^2 + x^2 + x + x + 1`

`x^3 + 1x^2 + 1x^2 + 1x + 1x + 1`

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

`x^3 + 2x^2 + 2x + 1`