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

1 Answer
smendyka
Mar 12, 2017

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

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