Basic Math Examples

$(3 y^{4} z^{2} - 2 y) (- 7 y z^{5})$

Step 1

Apply the distributive property.

$3 y^{4} z^{2} (- 7 y z^{5}) - 2 y (- 7 y z^{5})$

Step 2

Multiply $y^{4}$ by $y$ by adding the exponents.

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Step 2.1

Move $y$ .

$3 (y \cdot y^{4}) z^{2} (- 7 z^{5}) - 2 y (- 7 y z^{5})$

Step 2.2

Multiply $y$ by $y^{4}$ .

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Step 2.2.1

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

$3 (y^{1} y^{4}) z^{2} (- 7 z^{5}) - 2 y (- 7 y z^{5})$

Step 2.2.2

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

$3 y^{1 + 4} z^{2} (- 7 z^{5}) - 2 y (- 7 y z^{5})$

Step 2.3

Add $1$ and $4$ .

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

Step 3

Multiply $y$ by $y$ by adding the exponents.

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Step 3.1

Move $y$ .

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

Step 3.2

Multiply $y$ by $y$ .

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

Step 4

Simplify each term.

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Step 4.1

Multiply $z^{2}$ by $z^{5}$ by adding the exponents.

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Step 4.1.1

Move $z^{5}$ .

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

Step 4.1.2

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

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

Step 4.1.3

Add $5$ and $2$ .

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

Step 4.2

Multiply $- 7$ by $3$ .

$- 21 y^{5} z^{7} - 2 y^{2} (- 7 z^{5})$

Step 4.3

Rewrite using the commutative property of multiplication.

$- 21 y^{5} z^{7} - 2 \cdot - 7 y^{2} z^{5}$

Step 4.4

Multiply $- 2$ by $- 7$ .

$- 21 y^{5} z^{7} + 14 y^{2} z^{5}$