Basic Math Examples

$- 3 z y^{2} (9 z^{5} + 2 z^{3} y^{6} - 7 y^{6})$

Step 1

Apply the distributive property.

$- 3 z y^{2} (9 z^{5}) - 3 z y^{2} (2 z^{3} y^{6}) - 3 z y^{2} (- 7 y^{6})$

Step 2

Simplify.

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Step 2.1

Multiply $z$ by $z^{5}$ by adding the exponents.

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Step 2.1.1

Move $z^{5}$ .

$- 3 (z^{5} z) y^{2} \cdot 9 - 3 z y^{2} (2 z^{3} y^{6}) - 3 z y^{2} (- 7 y^{6})$

Step 2.1.2

Multiply $z^{5}$ by $z$ .

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Step 2.1.2.1

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

$- 3 (z^{5} z^{1}) y^{2} \cdot 9 - 3 z y^{2} (2 z^{3} y^{6}) - 3 z y^{2} (- 7 y^{6})$

Step 2.1.2.2

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

$- 3 z^{5 + 1} y^{2} \cdot 9 - 3 z y^{2} (2 z^{3} y^{6}) - 3 z y^{2} (- 7 y^{6})$

Step 2.1.3

Add $5$ and $1$ .

$- 3 z^{6} y^{2} \cdot 9 - 3 z y^{2} (2 z^{3} y^{6}) - 3 z y^{2} (- 7 y^{6})$

Step 2.2

Multiply $z$ by $z^{3}$ by adding the exponents.

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Step 2.2.1

Move $z^{3}$ .

$- 3 z^{6} y^{2} \cdot 9 - 3 (z^{3} z) y^{2} (2 y^{6}) - 3 z y^{2} (- 7 y^{6})$

Step 2.2.2

Multiply $z^{3}$ by $z$ .

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Step 2.2.2.1

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

$- 3 z^{6} y^{2} \cdot 9 - 3 (z^{3} z^{1}) y^{2} (2 y^{6}) - 3 z y^{2} (- 7 y^{6})$

Step 2.2.2.2

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

$- 3 z^{6} y^{2} \cdot 9 - 3 z^{3 + 1} y^{2} (2 y^{6}) - 3 z y^{2} (- 7 y^{6})$

Step 2.2.3

Add $3$ and $1$ .

$- 3 z^{6} y^{2} \cdot 9 - 3 z^{4} y^{2} (2 y^{6}) - 3 z y^{2} (- 7 y^{6})$

Step 2.3

Multiply $y^{2}$ by $y^{6}$ by adding the exponents.

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Step 2.3.1

Move $y^{6}$ .

$- 3 z^{6} y^{2} \cdot 9 - 3 z^{4} y^{2} (2 y^{6}) - 3 z (y^{6} y^{2}) \cdot - 7$

Step 2.3.2

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

$- 3 z^{6} y^{2} \cdot 9 - 3 z^{4} y^{2} (2 y^{6}) - 3 z y^{6 + 2} \cdot - 7$

Step 2.3.3

Add $6$ and $2$ .

$- 3 z^{6} y^{2} \cdot 9 - 3 z^{4} y^{2} (2 y^{6}) - 3 z y^{8} \cdot - 7$

Step 3

Simplify each term.

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Step 3.1

Multiply $9$ by $- 3$ .

$- 27 z^{6} y^{2} - 3 z^{4} y^{2} (2 y^{6}) - 3 z y^{8} \cdot - 7$

Step 3.2

Multiply $y^{2}$ by $y^{6}$ by adding the exponents.

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Step 3.2.1

Move $y^{6}$ .

$- 27 z^{6} y^{2} - 3 z^{4} (y^{6} y^{2}) \cdot 2 - 3 z y^{8} \cdot - 7$

Step 3.2.2

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

$- 27 z^{6} y^{2} - 3 z^{4} y^{6 + 2} \cdot 2 - 3 z y^{8} \cdot - 7$

Step 3.2.3

Add $6$ and $2$ .

$- 27 z^{6} y^{2} - 3 z^{4} y^{8} \cdot 2 - 3 z y^{8} \cdot - 7$

Step 3.3

Multiply $2$ by $- 3$ .

$- 27 z^{6} y^{2} - 6 z^{4} y^{8} - 3 z y^{8} \cdot - 7$

Step 3.4

Multiply $- 7$ by $- 3$ .

$- 27 z^{6} y^{2} - 6 z^{4} y^{8} + 21 z y^{8}$