Basic Math Examples

$2 - 6 (1 + 2 z - 3 z^{2}) \cdot (2 + 2 z)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$2 + (- 6 \cdot 1 - 6 (2 z) - 6 (- 3 z^{2})) \cdot (2 + 2 z)$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- 6$ by $1$ .

$2 + (- 6 - 6 (2 z) - 6 (- 3 z^{2})) \cdot (2 + 2 z)$

Step 1.2.2

Multiply $2$ by $- 6$ .

$2 + (- 6 - 12 z - 6 (- 3 z^{2})) \cdot (2 + 2 z)$

Step 1.2.3

Multiply $- 3$ by $- 6$ .

$2 + (- 6 - 12 z + 18 z^{2}) \cdot (2 + 2 z)$

Step 1.3

Expand $(- 6 - 12 z + 18 z^{2}) (2 + 2 z)$ by multiplying each term in the first expression by each term in the second expression.

$2 - 6 \cdot 2 - 6 (2 z) - 12 z \cdot 2 - 12 z (2 z) + 18 z^{2} \cdot 2 + 18 z^{2} (2 z)$

Step 1.4

Simplify each term.

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Step 1.4.1

Multiply $- 6$ by $2$ .

$2 - 12 - 6 (2 z) - 12 z \cdot 2 - 12 z (2 z) + 18 z^{2} \cdot 2 + 18 z^{2} (2 z)$

Step 1.4.2

Multiply $2$ by $- 6$ .

$2 - 12 - 12 z - 12 z \cdot 2 - 12 z (2 z) + 18 z^{2} \cdot 2 + 18 z^{2} (2 z)$

Step 1.4.3

Multiply $2$ by $- 12$ .

$2 - 12 - 12 z - 24 z - 12 z (2 z) + 18 z^{2} \cdot 2 + 18 z^{2} (2 z)$

Step 1.4.4

Rewrite using the commutative property of multiplication.

$2 - 12 - 12 z - 24 z - 12 \cdot 2 z \cdot z + 18 z^{2} \cdot 2 + 18 z^{2} (2 z)$

Step 1.4.5

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

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Step 1.4.5.1

Move $z$ .

$2 - 12 - 12 z - 24 z - 12 \cdot 2 (z \cdot z) + 18 z^{2} \cdot 2 + 18 z^{2} (2 z)$

Step 1.4.5.2

Multiply $z$ by $z$ .

$2 - 12 - 12 z - 24 z - 12 \cdot 2 z^{2} + 18 z^{2} \cdot 2 + 18 z^{2} (2 z)$

Step 1.4.6

Multiply $- 12$ by $2$ .

$2 - 12 - 12 z - 24 z - 24 z^{2} + 18 z^{2} \cdot 2 + 18 z^{2} (2 z)$

Step 1.4.7

Multiply $2$ by $18$ .

$2 - 12 - 12 z - 24 z - 24 z^{2} + 36 z^{2} + 18 z^{2} (2 z)$

Step 1.4.8

Rewrite using the commutative property of multiplication.

$2 - 12 - 12 z - 24 z - 24 z^{2} + 36 z^{2} + 18 \cdot 2 z^{2} z$

Step 1.4.9

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

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Step 1.4.9.1

Move $z$ .

$2 - 12 - 12 z - 24 z - 24 z^{2} + 36 z^{2} + 18 \cdot 2 (z \cdot z^{2})$

Step 1.4.9.2

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

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Step 1.4.9.2.1

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

$2 - 12 - 12 z - 24 z - 24 z^{2} + 36 z^{2} + 18 \cdot 2 (z^{1} z^{2})$

Step 1.4.9.2.2

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

$2 - 12 - 12 z - 24 z - 24 z^{2} + 36 z^{2} + 18 \cdot 2 z^{1 + 2}$

Step 1.4.9.3

Add $1$ and $2$ .

$2 - 12 - 12 z - 24 z - 24 z^{2} + 36 z^{2} + 18 \cdot 2 z^{3}$

Step 1.4.10

Multiply $18$ by $2$ .

$2 - 12 - 12 z - 24 z - 24 z^{2} + 36 z^{2} + 36 z^{3}$

Step 1.5

Subtract $24 z$ from $- 12 z$ .

$2 - 12 - 36 z - 24 z^{2} + 36 z^{2} + 36 z^{3}$

Step 1.6

Add $- 24 z^{2}$ and $36 z^{2}$ .

$2 - 12 - 36 z + 12 z^{2} + 36 z^{3}$

Step 2

Subtract $12$ from $2$ .

$- 10 - 36 z + 12 z^{2} + 36 z^{3}$