Write in Standard Form 7c(c^3-2c^2+5)

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

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Apply the distributive property.

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

Step 3

Simplify.

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

Move $c^{3}$ .

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

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

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

$7 (c^{3} c^{1}) + 7 c (- 2 c^{2}) + 7 c \cdot 5$

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

$7 c^{3 + 1} + 7 c (- 2 c^{2}) + 7 c \cdot 5$

Add $3$ and $1$ .

$7 c^{4} + 7 c (- 2 c^{2}) + 7 c \cdot 5$

Rewrite using the commutative property of multiplication.

$7 c^{4} + 7 \cdot - 2 c \cdot c^{2} + 7 c \cdot 5$

Multiply $5$ by $7$ .

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

Step 4

Simplify each term.

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

Move $c^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $7$ by $- 2$ .

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