Simplify 7c(5-2c^2+c^3)

$7 c (5 - 2 c^{2} + c^{3})$

Step 1

Apply the distributive property.

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

Step 2

Simplify.

Multiply $5$ by $7$ .

$35 c + 7 c (- 2 c^{2}) + 7 c \cdot c^{3}$

Rewrite using the commutative property of multiplication.

$35 c + 7 \cdot - 2 c \cdot c^{2} + 7 c \cdot c^{3}$

Multiply $c$ by $c^{3}$ by adding the exponents.

Move $c^{3}$ .

$35 c + 7 \cdot - 2 c \cdot c^{2} + 7 (c^{3} c)$

Multiply $c^{3}$ by $c$ .

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

$35 c + 7 \cdot - 2 c \cdot c^{2} + 7 (c^{3} c^{1})$

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

$35 c + 7 \cdot - 2 c \cdot c^{2} + 7 c^{3 + 1}$

Add $3$ and $1$ .

$35 c + 7 \cdot - 2 c \cdot c^{2} + 7 c^{4}$

Step 3

Simplify each term.

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

Move $c^{2}$ .

$35 c + 7 \cdot - 2 (c^{2} c) + 7 c^{4}$

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

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

$35 c + 7 \cdot - 2 (c^{2} c^{1}) + 7 c^{4}$

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

$35 c + 7 \cdot - 2 c^{2 + 1} + 7 c^{4}$

Add $2$ and $1$ .

$35 c + 7 \cdot - 2 c^{3} + 7 c^{4}$

Multiply $7$ by $- 2$ .

$35 c - 14 c^{3} + 7 c^{4}$