Pre-Algebra Examples

$\frac{c^{2} - 20 c + 100}{c - 10}$

Step 1

Factor using the perfect square rule.

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Step 1.1

Rewrite $100$ as $10^{2}$ .

$\frac{c^{2} - 20 c + 10^{2}}{c - 10}$

Step 1.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$20 c = 2 \cdot c \cdot 10$

Step 1.3

Rewrite the polynomial.

$\frac{c^{2} - 2 \cdot c \cdot 10 + 10^{2}}{c - 10}$

Step 1.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = c$ and $b = 10$ .

$\frac{{(c - 10)}^{2}}{c - 10}$

Step 2

Cancel the common factor of ${(c - 10)}^{2}$ and $c - 10$ .

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Step 2.1

Factor $c - 10$ out of ${(c - 10)}^{2}$ .

$\frac{(c - 10) (c - 10)}{c - 10}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Multiply by $1$ .

$\frac{(c - 10) (c - 10)}{(c - 10) \cdot 1}$

Step 2.2.2

Cancel the common factor.

$\frac{(c - 10) (c - 10)}{(c - 10) \cdot 1}$

Step 2.2.3

Rewrite the expression.

$\frac{c - 10}{1}$

Step 2.2.4

Divide $c - 10$ by $1$ .

$c - 10$