Simplify (4n-5)(n^2-7n-2)

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

Step 1

Expand $(4 n - 5) (n^{2} - 7 n - 2)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

Simplify each term.

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

Move $n^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $n$ .

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

Multiply $n$ by $n$ .

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

Multiply $4$ by $- 7$ .

$4 n^{3} - 28 n^{2} + 4 n \cdot - 2 - 5 n^{2} - 5 (- 7 n) - 5 \cdot - 2$

Multiply $- 2$ by $4$ .

$4 n^{3} - 28 n^{2} - 8 n - 5 n^{2} - 5 (- 7 n) - 5 \cdot - 2$

Multiply $- 7$ by $- 5$ .

$4 n^{3} - 28 n^{2} - 8 n - 5 n^{2} + 35 n - 5 \cdot - 2$

Multiply $- 5$ by $- 2$ .

$4 n^{3} - 28 n^{2} - 8 n - 5 n^{2} + 35 n + 10$

Simplify by adding terms.

Subtract $5 n^{2}$ from $- 28 n^{2}$ .

$4 n^{3} - 33 n^{2} - 8 n + 35 n + 10$

Add $- 8 n$ and $35 n$ .

$4 n^{3} - 33 n^{2} + 27 n + 10$