The problem asks us to expand the expression $6z^2(7z^2 + 3z - 2)$ and write the answer as a polynomial in standard form.

1. Problem Description

The problem asks us to expand the expression $6z^2(7z^2 + 3z - 2)$ and write the answer as a polynomial in standard form.

2. Solution Steps

To expand the expression, we need to distribute the term $6z^2$ to each term inside the parentheses.

$6z^2(7z^2 + 3z - 2) = 6z^2(7z^2) + 6z^2(3z) + 6z^2(-2)$

Now, we multiply each term:

$6z^2(7z^2) = (6 \times 7)(z^2 \times z^2) = 42z^{2+2} = 42z^4$

$6z^2(3z) = (6 \times 3)(z^2 \times z) = 18z^{2+1} = 18z^3$

$6z^2(-2) = (6 \times -2)(z^2) = -12z^2$

Combining these terms, we get:

$42z^4 + 18z^3 - 12z^2$

The polynomial is already in standard form, as the exponents are in decreasing order.

3. Final Answer

$42z^4 + 18z^3 - 12z^2$