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

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

Step 1

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

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

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $n$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $2$ by $4$ .

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

Multiply $- 5$ by $2$ .

$8 n^{3} - 10 n^{2} + 4 n (4 n) + 4 n \cdot - 5 + 4 (4 n) + 4 \cdot - 5$

Rewrite using the commutative property of multiplication.

$8 n^{3} - 10 n^{2} + 4 \cdot 4 n \cdot n + 4 n \cdot - 5 + 4 (4 n) + 4 \cdot - 5$

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

Move $n$ .

$8 n^{3} - 10 n^{2} + 4 \cdot 4 (n \cdot n) + 4 n \cdot - 5 + 4 (4 n) + 4 \cdot - 5$

Multiply $n$ by $n$ .

$8 n^{3} - 10 n^{2} + 4 \cdot 4 n^{2} + 4 n \cdot - 5 + 4 (4 n) + 4 \cdot - 5$

Multiply $4$ by $4$ .

$8 n^{3} - 10 n^{2} + 16 n^{2} + 4 n \cdot - 5 + 4 (4 n) + 4 \cdot - 5$

Multiply $- 5$ by $4$ .

$8 n^{3} - 10 n^{2} + 16 n^{2} - 20 n + 4 (4 n) + 4 \cdot - 5$

Multiply $4$ by $4$ .

$8 n^{3} - 10 n^{2} + 16 n^{2} - 20 n + 16 n + 4 \cdot - 5$

Multiply $4$ by $- 5$ .

$8 n^{3} - 10 n^{2} + 16 n^{2} - 20 n + 16 n - 20$

Simplify by adding terms.

Add $- 10 n^{2}$ and $16 n^{2}$ .

$8 n^{3} + 6 n^{2} - 20 n + 16 n - 20$

Add $- 20 n$ and $16 n$ .

$8 n^{3} + 6 n^{2} - 4 n - 20$