Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

Add $2$ and $2$ .

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

Step 2.2

Rewrite using the commutative property of multiplication.

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

Step 2.3

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

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

Step 3

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

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Step 3.1

Move $c$ .

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.3

Add $1$ and $2$ .

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

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