Write in Standard Form c^2(c^2-10c+25)

$c^{2} (c^{2} - 10 c + 25)$

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.

$c^{2} c^{2} + c^{2} (- 10 c) + c^{2} \cdot 25$

Step 3

Simplify.

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

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

$c^{2 + 2} + c^{2} (- 10 c) + c^{2} \cdot 25$

Add $2$ and $2$ .

$c^{4} + c^{2} (- 10 c) + c^{2} \cdot 25$

Rewrite using the commutative property of multiplication.

$c^{4} - 10 c^{2} c + c^{2} \cdot 25$

Move $25$ to the left of $c^{2}$ .

$c^{4} - 10 c^{2} c + 25 \cdot c^{2}$

Step 4

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

Move $c$ .

$c^{4} - 10 (c \cdot c^{2}) + 25 \cdot c^{2}$

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

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

$c^{4} - 10 (c^{1} c^{2}) + 25 \cdot c^{2}$

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

$c^{4} - 10 c^{1 + 2} + 25 \cdot c^{2}$

Add $1$ and $2$ .

$c^{4} - 10 c^{3} + 25 \cdot c^{2}$

$c^{4} - 10 c^{3} + 25 c^{2}$