Question

How do you multiply `2z(3z+2)(z-1)-(z+7)(z-9)`?

Answer 1

Use the distributive property and FOIL and combine like terms to get our answer, `6z^3-3z^2-2z+63`.

Explanation:

Let's split this into two parts. Focusing on the first part, `2z(3z+2)(z-1)`, we can use the distributive property to simplify it:

`2z(3z+2)(z-1)` = `(6z^2+4z)(z-1)`

Next, let's use FOIL to get to its simplest form:

`(6z^2)(z)+(6z^2)(-1)+(4z)(z)+(4z)(-1)`
`6z^3-6z^2+4z^2-4z`
`6z^3-2z^2-4z`

Let's also use FOIL to simplify the other half of our expression:

`(z+7)(z-9)`
`z^2-9z+7z-63`
`z^2-2z-63`

Finally, let's combine the two terms and simplify:

`6z^3-2z^2-4z-(z^2-2z-63)`
`6z^3-2z^2-4z-z^2+2z+63`
`6z^3-2z^2-z^2-4z+2z+63`
`6z^3-3z^2-2z+63`