Basic Math Examples

$(5 y^{6} Z^{5} - 4 Z) (- 9 y^{2} Z)$

Step 1

Apply the distributive property.

$5 y^{6} Z^{5} (- 9 y^{2} Z) - 4 Z (- 9 y^{2} Z)$

Step 2

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

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Step 2.1

Move $y^{2}$ .

$5 (y^{2} y^{6}) Z^{5} (- 9 Z) - 4 Z (- 9 y^{2} Z)$

Step 2.2

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

$5 y^{2 + 6} Z^{5} (- 9 Z) - 4 Z (- 9 y^{2} Z)$

Step 2.3

Add $2$ and $6$ .

$5 y^{8} Z^{5} (- 9 Z) - 4 Z (- 9 y^{2} Z)$

Step 3

Multiply $Z$ by $Z$ by adding the exponents.

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Step 3.1

Move $Z$ .

$5 y^{8} Z^{5} (- 9 Z) - 4 (Z \cdot Z) (- 9 y^{2})$

Step 3.2

Multiply $Z$ by $Z$ .

$5 y^{8} Z^{5} (- 9 Z) - 4 Z^{2} (- 9 y^{2})$

Step 4

Simplify each term.

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Step 4.1

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

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Step 4.1.1

Move $Z$ .

$5 y^{8} (Z \cdot Z^{5}) \cdot - 9 - 4 Z^{2} (- 9 y^{2})$

Step 4.1.2

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

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Step 4.1.2.1

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

$5 y^{8} (Z^{1} Z^{5}) \cdot - 9 - 4 Z^{2} (- 9 y^{2})$

Step 4.1.2.2

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

$5 y^{8} Z^{1 + 5} \cdot - 9 - 4 Z^{2} (- 9 y^{2})$

Step 4.1.3

Add $1$ and $5$ .

$5 y^{8} Z^{6} \cdot - 9 - 4 Z^{2} (- 9 y^{2})$

Step 4.2

Multiply $- 9$ by $5$ .

$- 45 y^{8} Z^{6} - 4 Z^{2} (- 9 y^{2})$

Step 4.3

Rewrite using the commutative property of multiplication.

$- 45 y^{8} Z^{6} - 4 \cdot - 9 Z^{2} y^{2}$

Step 4.4

Multiply $- 4$ by $- 9$ .

$- 45 y^{8} Z^{6} + 36 Z^{2} y^{2}$