Basic Math Examples

$\frac{(z - 4) (z + 8)}{2 z^{8}} \div \frac{7 z - 28}{14 z^{9}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{(z - 4) (z + 8)}{2 z^{8}} \cdot \frac{14 z^{9}}{7 z - 28}$

Step 2

Cancel the common factor of $2 z^{8}$ .

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Step 2.1

Factor $2 z^{8}$ out of $14 z^{9}$ .

$\frac{(z - 4) (z + 8)}{2 z^{8}} \cdot \frac{2 z^{8} (7 z)}{7 z - 28}$

Step 2.2

Cancel the common factor.

$\frac{(z - 4) (z + 8)}{2 z^{8}} \cdot \frac{2 z^{8} (7 z)}{7 z - 28}$

Step 2.3

Rewrite the expression.

$(z - 4) (z + 8) \frac{7 z}{7 z - 28}$

Step 3

Expand $(z - 4) (z + 8)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$(z (z + 8) - 4 (z + 8)) \frac{7 z}{7 z - 28}$

Step 3.2

Apply the distributive property.

$(z \cdot z + z \cdot 8 - 4 (z + 8)) \frac{7 z}{7 z - 28}$

Step 3.3

Apply the distributive property.

$(z \cdot z + z \cdot 8 - 4 z - 4 \cdot 8) \frac{7 z}{7 z - 28}$

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $z$ by $z$ .

$(z^{2} + z \cdot 8 - 4 z - 4 \cdot 8) \frac{7 z}{7 z - 28}$

Step 4.1.2

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

$(z^{2} + 8 \cdot z - 4 z - 4 \cdot 8) \frac{7 z}{7 z - 28}$

Step 4.1.3

Multiply $- 4$ by $8$ .

$(z^{2} + 8 z - 4 z - 32) \frac{7 z}{7 z - 28}$

Step 4.2

Subtract $4 z$ from $8 z$ .

$(z^{2} + 4 z - 32) \frac{7 z}{7 z - 28}$

Step 5

Simplify terms.

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Step 5.1

Factor $7$ out of $7 z - 28$ .

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Step 5.1.1

Factor $7$ out of $7 z$ .

$(z^{2} + 4 z - 32) \frac{7 z}{7 (z) - 28}$

Step 5.1.2

Factor $7$ out of $- 28$ .

$(z^{2} + 4 z - 32) \frac{7 z}{7 z + 7 \cdot - 4}$

Step 5.1.3

Factor $7$ out of $7 z + 7 \cdot - 4$ .

$(z^{2} + 4 z - 32) \frac{7 z}{7 (z - 4)}$

Step 5.2

Cancel the common factor of $7$ .

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Step 5.2.1

Cancel the common factor.

$(z^{2} + 4 z - 32) \frac{7 z}{7 (z - 4)}$

Step 5.2.2

Rewrite the expression.

$(z^{2} + 4 z - 32) \frac{z}{z - 4}$

Step 5.3

Multiply $z^{2} + 4 z - 32$ by $\frac{z}{z - 4}$ .

$\frac{(z^{2} + 4 z - 32) z}{z - 4}$

Step 6

Factor $z^{2} + 4 z - 32$ using the AC method.

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Step 6.1

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 $- 32$ and whose sum is $4$ .

$- 4, 8$

Step 6.2

Write the factored form using these integers.

$\frac{(z - 4) (z + 8) z}{z - 4}$

Step 7

Simplify terms.

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Step 7.1

Cancel the common factor of $z - 4$ .

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Step 7.1.1

Cancel the common factor.

$\frac{(z - 4) (z + 8) z}{z - 4}$

Step 7.1.2

Divide $(z + 8) z$ by $1$ .

$(z + 8) z$

Step 7.2

Apply the distributive property.

$z \cdot z + 8 z$

Step 7.3

Multiply $z$ by $z$ .

$z^{2} + 8 z$