0. $$ \quad 2(8 p-3 q)\left(p-3+q^{2}\right) $$

Question

UpStudy AI · Accepted Answer

To expand the expression:

$$
2(8p - 3q)\left(p - 3 + q^{2}\right)
$$

follow these steps:

### Step 1: Expand the Inner Product

First, expand the product $$(8p - 3q)(p - 3 + q^{2})$$:

$$
(8p - 3q)(p - 3 + q^{2}) = 8p \cdot p + 8p \cdot (-3) + 8p \cdot q^{2} - 3q \cdot p - 3q \cdot (-3) - 3q \cdot q^{2}
$$

Calculate each term:

$$
\begin{align*}
8p \cdot p &= 8p^{2} \
8p \cdot (-3) &= -24p \
8p \cdot q^{2} &= 8p q^{2} \
-3q \cdot p &= -3p q \
-3q \cdot (-3) &= 9q \
-3q \cdot q^{2} &= -3q^{3} \
\end{align*}
$$

Combine all the terms:

$$
8p^{2} - 24p + 8p q^{2} - 3p q + 9q - 3q^{3}
$$

### Step 2: Multiply by 2

Now, multiply the entire expression by 2:

$$
2 \times (8p^{2} - 24p + 8p q^{2} - 3p q + 9q - 3q^{3}) = 16p^{2} - 48p + 16p q^{2} - 6p q + 18q - 6q^{3}
$$

### Final Expanded Form

The fully expanded form of the original expression is:

$$
16p^{2} - 48p + 16p q^{2} - 6p q + 18q - 6q^{3}
$$
The expanded form of the expression $$ 2(8p - 3q)(p - 3 + q^{2}) $$ is: $$ 16p^{2} - 48p + 16p q^{2} - 6p q + 18q - 6q^{3} $$

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