Find the Product 4n(5n^2-7n-3)

$4 n (5 n^{2} - 7 n - 3)$

Step 1

Apply the distributive property.

$4 n (5 n^{2}) + 4 n (- 7 n) + 4 n \cdot - 3$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$4 \cdot 5 n \cdot n^{2} + 4 n (- 7 n) + 4 n \cdot - 3$

Rewrite using the commutative property of multiplication.

$4 \cdot 5 n \cdot n^{2} + 4 \cdot - 7 n \cdot n + 4 n \cdot - 3$

Multiply $- 3$ by $4$ .

$4 \cdot 5 n \cdot n^{2} + 4 \cdot - 7 n \cdot n - 12 n$

Step 3

Simplify each term.

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

Move $n^{2}$ .

$4 \cdot 5 (n^{2} n) + 4 \cdot - 7 n \cdot n - 12 n$

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

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

$4 \cdot 5 (n^{2} n^{1}) + 4 \cdot - 7 n \cdot n - 12 n$

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

$4 \cdot 5 n^{2 + 1} + 4 \cdot - 7 n \cdot n - 12 n$

Add $2$ and $1$ .

$4 \cdot 5 n^{3} + 4 \cdot - 7 n \cdot n - 12 n$

Multiply $4$ by $5$ .

$20 n^{3} + 4 \cdot - 7 n \cdot n - 12 n$

Multiply $n$ by $n$ by adding the exponents.

Move $n$ .

$20 n^{3} + 4 \cdot - 7 (n \cdot n) - 12 n$

Multiply $n$ by $n$ .

$20 n^{3} + 4 \cdot - 7 n^{2} - 12 n$

Multiply $4$ by $- 7$ .

$20 n^{3} - 28 n^{2} - 12 n$