Basic Math Examples

$(3 w^{2} - 6 w^{3} + 7) \cdot (5 w^{5})$

Step 1

Apply the distributive property.

$3 w^{2} (5 w^{5}) - 6 w^{3} (5 w^{5}) + 7 (5 w^{5})$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$3 \cdot 5 w^{2} w^{5} - 6 w^{3} (5 w^{5}) + 7 (5 w^{5})$

Step 2.2

Rewrite using the commutative property of multiplication.

$3 \cdot 5 w^{2} w^{5} - 6 \cdot 5 w^{3} w^{5} + 7 (5 w^{5})$

Step 2.3

Multiply $5$ by $7$ .

$3 \cdot 5 w^{2} w^{5} - 6 \cdot 5 w^{3} w^{5} + 35 w^{5}$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $w^{5}$ .

$3 \cdot 5 (w^{5} w^{2}) - 6 \cdot 5 w^{3} w^{5} + 35 w^{5}$

Step 3.1.2

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

$3 \cdot 5 w^{5 + 2} - 6 \cdot 5 w^{3} w^{5} + 35 w^{5}$

Step 3.1.3

Add $5$ and $2$ .

$3 \cdot 5 w^{7} - 6 \cdot 5 w^{3} w^{5} + 35 w^{5}$

Step 3.2

Multiply $3$ by $5$ .

$15 w^{7} - 6 \cdot 5 w^{3} w^{5} + 35 w^{5}$

Step 3.3

Multiply $w^{3}$ by $w^{5}$ by adding the exponents.

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Step 3.3.1

Move $w^{5}$ .

$15 w^{7} - 6 \cdot 5 (w^{5} w^{3}) + 35 w^{5}$

Step 3.3.2

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

$15 w^{7} - 6 \cdot 5 w^{5 + 3} + 35 w^{5}$

Step 3.3.3

Add $5$ and $3$ .

$15 w^{7} - 6 \cdot 5 w^{8} + 35 w^{5}$

Step 3.4

Multiply $- 6$ by $5$ .

$15 w^{7} - 30 w^{8} + 35 w^{5}$

Step 4

Reorder $15 w^{7}$ and $- 30 w^{8}$ .

$- 30 w^{8} + 15 w^{7} + 35 w^{5}$