Basic Math Examples

$(10 z^{3} - 8 z^{5} + 5) \cdot (7 z^{4})$

Step 1

Apply the distributive property.

$10 z^{3} (7 z^{4}) - 8 z^{5} (7 z^{4}) + 5 (7 z^{4})$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$10 \cdot 7 z^{3} z^{4} - 8 z^{5} (7 z^{4}) + 5 (7 z^{4})$

Step 2.2

Rewrite using the commutative property of multiplication.

$10 \cdot 7 z^{3} z^{4} - 8 \cdot 7 z^{5} z^{4} + 5 (7 z^{4})$

Step 2.3

Multiply $7$ by $5$ .

$10 \cdot 7 z^{3} z^{4} - 8 \cdot 7 z^{5} z^{4} + 35 z^{4}$

Step 3

Simplify each term.

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Step 3.1

Multiply $z^{3}$ by $z^{4}$ by adding the exponents.

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Step 3.1.1

Move $z^{4}$ .

$10 \cdot 7 (z^{4} z^{3}) - 8 \cdot 7 z^{5} z^{4} + 35 z^{4}$

Step 3.1.2

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

$10 \cdot 7 z^{4 + 3} - 8 \cdot 7 z^{5} z^{4} + 35 z^{4}$

Step 3.1.3

Add $4$ and $3$ .

$10 \cdot 7 z^{7} - 8 \cdot 7 z^{5} z^{4} + 35 z^{4}$

Step 3.2

Multiply $10$ by $7$ .

$70 z^{7} - 8 \cdot 7 z^{5} z^{4} + 35 z^{4}$

Step 3.3

Multiply $z^{5}$ by $z^{4}$ by adding the exponents.

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Step 3.3.1

Move $z^{4}$ .

$70 z^{7} - 8 \cdot 7 (z^{4} z^{5}) + 35 z^{4}$

Step 3.3.2

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

$70 z^{7} - 8 \cdot 7 z^{4 + 5} + 35 z^{4}$

Step 3.3.3

Add $4$ and $5$ .

$70 z^{7} - 8 \cdot 7 z^{9} + 35 z^{4}$

Step 3.4

Multiply $- 8$ by $7$ .

$70 z^{7} - 56 z^{9} + 35 z^{4}$

Step 4

Reorder $70 z^{7}$ and $- 56 z^{9}$ .

$- 56 z^{9} + 70 z^{7} + 35 z^{4}$