Find the Product -6p^3(3p^2+5p-1)

$- 6 p^{3} (3 p^{2} + 5 p - 1)$

Apply the distributive property.

$- 6 p^{3} (3 p^{2}) - 6 p^{3} (5 p) - 6 p^{3} \cdot - 1$

Simplify.

Rewrite using the commutative property of multiplication.

$- 6 \cdot 3 p^{3} p^{2} - 6 p^{3} (5 p) - 6 p^{3} \cdot - 1$

Rewrite using the commutative property of multiplication.

$- 6 \cdot 3 p^{3} p^{2} - 6 \cdot 5 p^{3} p - 6 p^{3} \cdot - 1$

Multiply $- 1$ by $- 6$ .

$- 6 \cdot 3 p^{3} p^{2} - 6 \cdot 5 p^{3} p + 6 p^{3}$

Simplify each term.

Multiply $p^{3}$ by $p^{2}$ by adding the exponents.

Move $p^{2}$ .

$- 6 \cdot 3 (p^{2} p^{3}) - 6 \cdot 5 p^{3} p + 6 p^{3}$

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

$- 6 \cdot 3 p^{2 + 3} - 6 \cdot 5 p^{3} p + 6 p^{3}$

Add $2$ and $3$ .

$- 6 \cdot 3 p^{5} - 6 \cdot 5 p^{3} p + 6 p^{3}$

Multiply $- 6$ by $3$ .

$- 18 p^{5} - 6 \cdot 5 p^{3} p + 6 p^{3}$

Multiply $p^{3}$ by $p$ by adding the exponents.

Move $p$ .

$- 18 p^{5} - 6 \cdot 5 (p \cdot p^{3}) + 6 p^{3}$

Multiply $p$ by $p^{3}$ .

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

$- 18 p^{5} - 6 \cdot 5 (p^{1} p^{3}) + 6 p^{3}$

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

$- 18 p^{5} - 6 \cdot 5 p^{1 + 3} + 6 p^{3}$

Add $1$ and $3$ .

$- 18 p^{5} - 6 \cdot 5 p^{4} + 6 p^{3}$

Multiply $- 6$ by $5$ .

$- 18 p^{5} - 30 p^{4} + 6 p^{3}$