Question

How do you simplify `(3+ 8x ) ( 9- 8x + 7x ^ { 2} )`?

Answer 1

`56x^3` - `43x^2` + `48x` = 27

Explanation:

Multiply everything in the second bracket by everything in the first bracket then collect like terms.
`( 3 + 8x ) ( 9 - 8x + 7x^2 )`
first multiply the second bracket by 3;
`27 - 24x + 21x^2`
now multiply the second bracket by `8x`;
`72x - 64x^2 + 56x^3`
I would write this all on one line as I did it like so:

`27 - 24x + 21x^2 + 72x - 64x^2 +56x^3`

Now collect like terms so all the terms without `x` go together, all the terms with `x`, all the terms with `x^2` and all the terms with `x^3` etc

`27 + 48x - 43x^2 + 56x^3`

Then I rearranged it with the highest powers first (because I am a bit sad!)

`56x^3 - 43x^2 + 48x + 27`