Basic Math Examples

$\frac{z^{2} + 9 z}{5} \cdot \frac{16}{2 z + 18}$

Step 1

Factor $z$ out of $z^{2} + 9 z$ .

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Step 1.1

Factor $z$ out of $z^{2}$ .

$\frac{z \cdot z + 9 z}{5} \cdot \frac{16}{2 z + 18}$

Step 1.2

Factor $z$ out of $9 z$ .

$\frac{z \cdot z + z \cdot 9}{5} \cdot \frac{16}{2 z + 18}$

Step 1.3

Factor $z$ out of $z \cdot z + z \cdot 9$ .

$\frac{z (z + 9)}{5} \cdot \frac{16}{2 z + 18}$

Step 2

Factor $2$ out of $2 z + 18$ .

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Step 2.1

Factor $2$ out of $2 z$ .

$\frac{z (z + 9)}{5} \cdot \frac{16}{2 (z) + 18}$

Step 2.2

Factor $2$ out of $18$ .

$\frac{z (z + 9)}{5} \cdot \frac{16}{2 z + 2 \cdot 9}$

Step 2.3

Factor $2$ out of $2 z + 2 \cdot 9$ .

$\frac{z (z + 9)}{5} \cdot \frac{16}{2 (z + 9)}$

Step 3

Cancel the common factor of $z + 9$ .

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Step 3.1

Factor $z + 9$ out of $z (z + 9)$ .

$\frac{(z + 9) z}{5} \cdot \frac{16}{2 (z + 9)}$

Step 3.2

Factor $z + 9$ out of $2 (z + 9)$ .

$\frac{(z + 9) z}{5} \cdot \frac{16}{(z + 9) \cdot 2}$

Step 3.3

Cancel the common factor.

$\frac{(z + 9) z}{5} \cdot \frac{16}{(z + 9) \cdot 2}$

Step 3.4

Rewrite the expression.

$\frac{z}{5} \cdot \frac{16}{2}$

Step 4

Multiply $\frac{z}{5}$ by $\frac{16}{2}$ .

$\frac{z \cdot 16}{5 \cdot 2}$

Step 5

Multiply $5$ by $2$ .

$\frac{z \cdot 16}{10}$

Step 6

Cancel the common factor of $16$ and $10$ .

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Step 6.1

Factor $2$ out of $z \cdot 16$ .

$\frac{2 (z \cdot 8)}{10}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $10$ .

$\frac{2 (z \cdot 8)}{2 (5)}$

Step 6.2.2

Cancel the common factor.

$\frac{2 (z \cdot 8)}{2 \cdot 5}$

Step 6.2.3

Rewrite the expression.

$\frac{z \cdot 8}{5}$

Step 7

Move $8$ to the left of $z$ .

$\frac{8 z}{5}$