Question

What is the standard form of `y= (x + 2)(x^3 + 216)`?

Answer 1

See the entire solution process below>

Explanation:

We must multiply the two terms on the right to put this equation into standard form: To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`y = (color(red)(x) + color(red)(2))(color(blue)(x^3) + color(blue)(216))` becomes:

`y = (color(red)(x) xx color(blue)(x^3)) + (color(red)(x) xx color(blue)(216)) + (color(red)(2) xx color(blue)(x^3)) + (color(red)(2) xx color(blue)(216))`

`y = x^4 + 216x + 2x^3 + 432`

We can now put the `x` terms in descending order by power:

`y = x^4 + 2x^3 + 216x + 432`