Basic Math Examples

$8 z (z + 2) (z - 2)$

Step 1

Apply the distributive property.

$(8 z \cdot z + 8 z \cdot 2) (z - 2)$

Step 2

Multiply $z$ by $z$ by adding the exponents.

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Step 2.1

Move $z$ .

$(8 (z \cdot z) + 8 z \cdot 2) (z - 2)$

Step 2.2

Multiply $z$ by $z$ .

$(8 z^{2} + 8 z \cdot 2) (z - 2)$

Step 3

Multiply $2$ by $8$ .

$(8 z^{2} + 16 z) (z - 2)$

Step 4

Expand $(8 z^{2} + 16 z) (z - 2)$ using the FOIL Method.

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Step 4.1

Apply the distributive property.

$8 z^{2} (z - 2) + 16 z (z - 2)$

Step 4.2

Apply the distributive property.

$8 z^{2} z + 8 z^{2} \cdot - 2 + 16 z (z - 2)$

Step 4.3

Apply the distributive property.

$8 z^{2} z + 8 z^{2} \cdot - 2 + 16 z \cdot z + 16 z \cdot - 2$

Step 5

Simplify and combine like terms.

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Step 5.1

Simplify each term.

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Step 5.1.1

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

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Step 5.1.1.1

Move $z$ .

$8 (z \cdot z^{2}) + 8 z^{2} \cdot - 2 + 16 z \cdot z + 16 z \cdot - 2$

Step 5.1.1.2

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

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Step 5.1.1.2.1

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

$8 (z^{1} z^{2}) + 8 z^{2} \cdot - 2 + 16 z \cdot z + 16 z \cdot - 2$

Step 5.1.1.2.2

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

$8 z^{1 + 2} + 8 z^{2} \cdot - 2 + 16 z \cdot z + 16 z \cdot - 2$

Step 5.1.1.3

Add $1$ and $2$ .

$8 z^{3} + 8 z^{2} \cdot - 2 + 16 z \cdot z + 16 z \cdot - 2$

Step 5.1.2

Multiply $- 2$ by $8$ .

$8 z^{3} - 16 z^{2} + 16 z \cdot z + 16 z \cdot - 2$

Step 5.1.3

Multiply $z$ by $z$ by adding the exponents.

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Step 5.1.3.1

Move $z$ .

$8 z^{3} - 16 z^{2} + 16 (z \cdot z) + 16 z \cdot - 2$

Step 5.1.3.2

Multiply $z$ by $z$ .

$8 z^{3} - 16 z^{2} + 16 z^{2} + 16 z \cdot - 2$

Step 5.1.4

Multiply $- 2$ by $16$ .

$8 z^{3} - 16 z^{2} + 16 z^{2} - 32 z$

Step 5.2

Add $- 16 z^{2}$ and $16 z^{2}$ .

$8 z^{3} + 0 - 32 z$

Step 5.3

Add $8 z^{3}$ and $0$ .

$8 z^{3} - 32 z$