Simplify -p(8p^2+3p)

$- p (8 p^{2} + 3 p)$

Step 1

Simplify by multiplying through.

Apply the distributive property.

$- p (8 p^{2}) - p (3 p)$

Reorder.

Rewrite using the commutative property of multiplication.

$- 1 \cdot 8 p \cdot p^{2} - p (3 p)$

Rewrite using the commutative property of multiplication.

$- 1 \cdot 8 p \cdot p^{2} - 1 \cdot 3 p \cdot p$

Step 2

Simplify each term.

Multiply $p$ by $p^{2}$ by adding the exponents.

Move $p^{2}$ .

$- 1 \cdot 8 (p^{2} p) - 1 \cdot 3 p \cdot p$

Multiply $p^{2}$ by $p$ .

Raise $p$ to the power of $1$ .

$- 1 \cdot 8 (p^{2} p^{1}) - 1 \cdot 3 p \cdot p$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 1 \cdot 8 p^{2 + 1} - 1 \cdot 3 p \cdot p$

Add $2$ and $1$ .

$- 1 \cdot 8 p^{3} - 1 \cdot 3 p \cdot p$

Multiply $- 1$ by $8$ .

$- 8 p^{3} - 1 \cdot 3 p \cdot p$

Multiply $p$ by $p$ by adding the exponents.

Move $p$ .

$- 8 p^{3} - 1 \cdot 3 (p \cdot p)$

Multiply $p$ by $p$ .

$- 8 p^{3} - 1 \cdot 3 p^{2}$

Multiply $- 1$ by $3$ .

$- 8 p^{3} - 3 p^{2}$