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

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

Step 1

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

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

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $n$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $2$ by $2$ .

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

Multiply $- 4$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $n$ .

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

Multiply $n$ by $n$ .

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

Multiply $5$ by $2$ .

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

Multiply $- 4$ by $5$ .

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

Multiply $2$ by $4$ .

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

Multiply $4$ by $- 4$ .

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

Simplify by adding terms.

Add $- 8 n^{2}$ and $10 n^{2}$ .

$4 n^{3} + 2 n^{2} - 20 n + 8 n - 16$

Add $- 20 n$ and $8 n$ .

$4 n^{3} + 2 n^{2} - 12 n - 16$