Simplify (n+2)(n^2+5n-3)

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

Step 1

Expand $(n + 2) (n^{2} + 5 n - 3)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

Simplify each term.

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

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

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

$n^{1} n^{2} + n (5 n) + n \cdot - 3 + 2 n^{2} + 2 (5 n) + 2 \cdot - 3$

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

$n^{1 + 2} + n (5 n) + n \cdot - 3 + 2 n^{2} + 2 (5 n) + 2 \cdot - 3$

Add $1$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $n$ .

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

Multiply $n$ by $n$ .

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

Move $- 3$ to the left of $n$ .

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

Multiply $5$ by $2$ .

$n^{3} + 5 n^{2} - 3 n + 2 n^{2} + 10 n + 2 \cdot - 3$

Multiply $2$ by $- 3$ .

$n^{3} + 5 n^{2} - 3 n + 2 n^{2} + 10 n - 6$

Simplify by adding terms.

Add $5 n^{2}$ and $2 n^{2}$ .

$n^{3} + 7 n^{2} - 3 n + 10 n - 6$

Add $- 3 n$ and $10 n$ .

$n^{3} + 7 n^{2} + 7 n - 6$