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

1 Answer
Mar 12, 2017

Answer:

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#