Question

How do you multiply `(x^3+1)^2`?

Answer 1

See full explanation below:

Explanation:

This expression can be rewritten as:

`(color(red)(x^3 + 1))(color(blue)(x^3 + 1))`

We can next cross multiply each term in the parenthesis on the left by each term in the parenthesis on the right:

`(color(red)(x^3) xx color(blue)(x^3)) + (color(red)(x^3) xx color(blue)(1)) + (color(red)(1) xx color(blue)(x^3)) + (color(red)(1) xx color(blue)(1)) ->`

`x^6 + x^3 + x^3 + 1`

Now we can combine like terms:

`x^6 + 2x^3 + 1`