Question

multiply the polynomials.
(3z - 3)(9z² + 9z + 9) = \square

Explanation:

Step1: Apply distributive property (FOIL-like for polynomials)

Multiply \(3z\) by each term in \(9z^2 + 9z + 9\) and \(-3\) by each term in \(9z^2 + 9z + 9\).
\(3z \times 9z^2 = 27z^3\), \(3z \times 9z = 27z^2\), \(3z \times 9 = 27z\)
\(-3 \times 9z^2 = -27z^2\), \(-3 \times 9z = -27z\), \(-3 \times 9 = -27\)

Step2: Combine like terms

Now, combine the terms:
\(27z^3 + 27z^2 + 27z - 27z^2 - 27z - 27\)
The \(27z^2\) and \(-27z^2\) cancel out, and the \(27z\) and \(-27z\) cancel out.
We are left with \(27z^3 - 27\)

Answer:

\(27z^3 - 27\)