Find the Product -7p^3(4p^2+3p-1)

$- 7 p^{3} (4 p^{2} + 3 p - 1)$

Apply the distributive property.

$- 7 p^{3} (4 p^{2}) - 7 p^{3} (3 p) - 7 p^{3} \cdot - 1$

Simplify.

Rewrite using the commutative property of multiplication.

$- 7 \cdot 4 p^{3} p^{2} - 7 p^{3} (3 p) - 7 p^{3} \cdot - 1$

Rewrite using the commutative property of multiplication.

$- 7 \cdot 4 p^{3} p^{2} - 7 \cdot 3 p^{3} p - 7 p^{3} \cdot - 1$

Multiply $- 1$ by $- 7$ .

$- 7 \cdot 4 p^{3} p^{2} - 7 \cdot 3 p^{3} p + 7 p^{3}$

Simplify each term.

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

Move $p^{2}$ .

$- 7 \cdot 4 (p^{2} p^{3}) - 7 \cdot 3 p^{3} p + 7 p^{3}$

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

$- 7 \cdot 4 p^{2 + 3} - 7 \cdot 3 p^{3} p + 7 p^{3}$

Add $2$ and $3$ .

$- 7 \cdot 4 p^{5} - 7 \cdot 3 p^{3} p + 7 p^{3}$

Multiply $- 7$ by $4$ .

$- 28 p^{5} - 7 \cdot 3 p^{3} p + 7 p^{3}$

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

Move $p$ .

$- 28 p^{5} - 7 \cdot 3 (p \cdot p^{3}) + 7 p^{3}$

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

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

$- 28 p^{5} - 7 \cdot 3 (p^{1} p^{3}) + 7 p^{3}$

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

$- 28 p^{5} - 7 \cdot 3 p^{1 + 3} + 7 p^{3}$

Add $1$ and $3$ .

$- 28 p^{5} - 7 \cdot 3 p^{4} + 7 p^{3}$

Multiply $- 7$ by $3$ .

$- 28 p^{5} - 21 p^{4} + 7 p^{3}$