Basic Math Examples

$\frac{4 k^{2} - 12 k}{8} \cdot \frac{k - 6}{k^{2} - 9 k + 18}$

Step 1

Factor $4 k$ out of $4 k^{2} - 12 k$ .

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Step 1.1

Factor $4 k$ out of $4 k^{2}$ .

$\frac{4 k (k) - 12 k}{8} \cdot \frac{k - 6}{k^{2} - 9 k + 18}$

Step 1.2

Factor $4 k$ out of $- 12 k$ .

$\frac{4 k (k) + 4 k (- 3)}{8} \cdot \frac{k - 6}{k^{2} - 9 k + 18}$

Step 1.3

Factor $4 k$ out of $4 k (k) + 4 k (- 3)$ .

$\frac{4 k (k - 3)}{8} \cdot \frac{k - 6}{k^{2} - 9 k + 18}$

Step 2

Factor $k^{2} - 9 k + 18$ using the AC method.

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Step 2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $18$ and whose sum is $- 9$ .

$- 6, - 3$

Step 2.2

Write the factored form using these integers.

$\frac{4 k (k - 3)}{8} \cdot \frac{k - 6}{(k - 6) (k - 3)}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $k - 3$ .

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Step 3.1.1

Factor $k - 3$ out of $4 k (k - 3)$ .

$\frac{(k - 3) (4 k)}{8} \cdot \frac{k - 6}{(k - 6) (k - 3)}$

Step 3.1.2

Factor $k - 3$ out of $(k - 6) (k - 3)$ .

$\frac{(k - 3) (4 k)}{8} \cdot \frac{k - 6}{(k - 3) (k - 6)}$

Step 3.1.3

Cancel the common factor.

$\frac{(k - 3) (4 k)}{8} \cdot \frac{k - 6}{(k - 3) (k - 6)}$

Step 3.1.4

Rewrite the expression.

$\frac{4 k}{8} \cdot \frac{k - 6}{k - 6}$

Step 3.2

Multiply $\frac{4 k}{8}$ by $\frac{k - 6}{k - 6}$ .

$\frac{4 k (k - 6)}{8 (k - 6)}$

Step 3.3

Cancel the common factor of $4$ and $8$ .

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Step 3.3.1

Factor $4$ out of $4 k (k - 6)$ .

$\frac{4 (k (k - 6))}{8 (k - 6)}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor $4$ out of $8 (k - 6)$ .

$\frac{4 (k (k - 6))}{4 (2 (k - 6))}$

Step 3.3.2.2

Cancel the common factor.

$\frac{4 (k (k - 6))}{4 (2 (k - 6))}$

Step 3.3.2.3

Rewrite the expression.

$\frac{k (k - 6)}{2 (k - 6)}$

Step 3.4

Cancel the common factor of $k - 6$ .

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Step 3.4.1

Cancel the common factor.

$\frac{k (k - 6)}{2 (k - 6)}$

Step 3.4.2

Rewrite the expression.

$\frac{k}{2}$