Question

What is the standard form of `y= (x - 6)(x^2 + 6x + 36)`?

Answer 1

See the entire solution process below:

Explanation:

To multiply these two terms and put it into standard form you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`y = (color(red)(x) - color(red)(6))(color(blue)(x^2) + color(blue)(6x) + color(blue)(36))` becomes:

`y = (color(red)(x) xx color(blue)(x^2)) + (color(red)(x) xx color(blue)(6x)) + (color(red)(x) xx color(blue)(36)) - (color(red)(6) xx color(blue)(x^2)) - (color(red)(6) xx color(blue)(6x)) - (color(red)(6) xx color(blue)(36))`

`y = x^3 + 6x^2 + 36x - 6x^2 - 36x - 216`

We can now group and combine like terms and put into standard form:

`y = x^3 + 6x^2 - 6x^2 + 36x - 36x - 216`

`y = x^3 + (6x^2 - 6x^2) + (36x - 36x) - 216`

`y = x^3 + 0 + 0 - 216`

`y = x^3 - 216`