Simplify (c^2+2c-6)(c+5)

$(c^{2} + 2 c - 6) (c + 5)$

Step 1

Expand $(c^{2} + 2 c - 6) (c + 5)$ by multiplying each term in the first expression by each term in the second expression.

$c^{2} c + c^{2} \cdot 5 + 2 c \cdot c + 2 c \cdot 5 - 6 c - 6 \cdot 5$

Step 2

Simplify terms.

Simplify each term.

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

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

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

$c^{2} c^{1} + c^{2} \cdot 5 + 2 c \cdot c + 2 c \cdot 5 - 6 c - 6 \cdot 5$

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

$c^{2 + 1} + c^{2} \cdot 5 + 2 c \cdot c + 2 c \cdot 5 - 6 c - 6 \cdot 5$

Add $2$ and $1$ .

$c^{3} + c^{2} \cdot 5 + 2 c \cdot c + 2 c \cdot 5 - 6 c - 6 \cdot 5$

Move $5$ to the left of $c^{2}$ .

$c^{3} + 5 \cdot c^{2} + 2 c \cdot c + 2 c \cdot 5 - 6 c - 6 \cdot 5$

Multiply $c$ by $c$ by adding the exponents.

Move $c$ .

$c^{3} + 5 c^{2} + 2 (c \cdot c) + 2 c \cdot 5 - 6 c - 6 \cdot 5$

Multiply $c$ by $c$ .

$c^{3} + 5 c^{2} + 2 c^{2} + 2 c \cdot 5 - 6 c - 6 \cdot 5$

Multiply $5$ by $2$ .

$c^{3} + 5 c^{2} + 2 c^{2} + 10 c - 6 c - 6 \cdot 5$

Multiply $- 6$ by $5$ .

$c^{3} + 5 c^{2} + 2 c^{2} + 10 c - 6 c - 30$

Simplify by adding terms.

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

$c^{3} + 7 c^{2} + 10 c - 6 c - 30$

Subtract $6 c$ from $10 c$ .

$c^{3} + 7 c^{2} + 4 c - 30$