# How do you find the product of #(x + 1) (x^2 + x + 1)#?

##### 2 Answers

#### Answer:

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.

We can now group and combine like terms:

#### Answer:

#### Explanation:

The way I like to do it is longer to explain than to do...

Look at each possible power of

So in our example:

Given:

#(x+1)(x^2+x+1)#

we can tell that the highest possible power of

#1*1 = color(blue)(1)#

So we can start to write:

#(x+1)(x^2+x+1) = x^3...#

#1*1+1*1 = color(blue)(2)#

So we can add

#(x+1)(x^2+x+1) = x^3+2x^2...#

#1*1+1*1 = color(blue)(2)#

So we can add

#(x+1)(x^2+x+1) = x^3+2x^2+2x...#

#1*1 = color(blue)(1)#

So our final result is:

#(x+1)(x^2+x+1) = x^3+2x^2+2x+1#

In practice (and with practice) the result line is all you need write: Adding up the coefficients can be done in your head.