Find the Product -4n(-5n^3-1)

$- 4 n (- 5 n^{3} - 1)$

Simplify by multiplying through.

Apply the distributive property.

$- 4 n (- 5 n^{3}) - 4 n \cdot - 1$

Simplify the expression.

Rewrite using the commutative property of multiplication.

$- 4 \cdot - 5 n \cdot n^{3} - 4 n \cdot - 1$

Multiply $- 1$ by $- 4$ .

$- 4 \cdot - 5 n \cdot n^{3} + 4 n$

Simplify each term.

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

Move $n^{3}$ .

$- 4 \cdot - 5 (n^{3} n) + 4 n$

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

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

$- 4 \cdot - 5 (n^{3} n^{1}) + 4 n$

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

$- 4 \cdot - 5 n^{3 + 1} + 4 n$

Add $3$ and $1$ .

$- 4 \cdot - 5 n^{4} + 4 n$

Multiply $- 4$ by $- 5$ .

$20 n^{4} + 4 n$