Simplify c(3c^5+c+b-4)

$c (3 c^{5} + c + b - 4)$

Step 1

Apply the distributive property.

$c (3 c^{5}) + c \cdot c + c b + c \cdot - 4$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$3 c \cdot c^{5} + c \cdot c + c b + c \cdot - 4$

Multiply $c$ by $c$ .

$3 c \cdot c^{5} + c^{2} + c b + c \cdot - 4$

Move $- 4$ to the left of $c$ .

$3 c \cdot c^{5} + c^{2} + c b - 4 \cdot c$

Step 3

Multiply $c$ by $c^{5}$ by adding the exponents.

Move $c^{5}$ .

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

Multiply $c^{5}$ by $c$ .

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

$3 (c^{5} c^{1}) + c^{2} + c b - 4 \cdot c$

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

$3 c^{5 + 1} + c^{2} + c b - 4 \cdot c$

Add $5$ and $1$ .

$3 c^{6} + c^{2} + c b - 4 \cdot c$

$3 c^{6} + c^{2} + c b - 4 c$

Step 4

Simplify the expression.

Reorder $c$ and $b$ .

$3 c^{6} + c^{2} + b c - 4 c$

Move $c^{2}$ .

$3 c^{6} + b c + c^{2} - 4 c$