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

1 Answer
Jun 23, 2018

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