Question

find the product. simplify your answer.
$g^{2}(-3g^{2}-4g - 1)$

Explanation:

Step1: Distribute $g^2$ to each term

$g^2(-3g^2) + g^2(-4g) + g^2(-1)$

Step2: Multiply using exponent rules

When multiplying terms with the same base, add exponents: $a^m \cdot a^n = a^{m+n}$

$$\begin{align} g^2(-3g^2) &= -3g^{2+2} = -3g^4 \\ g^2(-4g) &= -4g^{2+1} = -4g^3 \\ g^2(-1) &= -g^2 \end{align}$$

Step3: Combine the resulting terms

$-3g^4 - 4g^3 - g^2$

Answer:

$-3g^4 - 4g^3 - g^2$