Pre-Algebra Examples

$(10 w^{5} - 3 w^{3} + 5) \cdot (4 w^{4})$

Step 1

Apply the distributive property.

$10 w^{5} (4 w^{4}) - 3 w^{3} (4 w^{4}) + 5 (4 w^{4})$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$10 \cdot 4 w^{5} w^{4} - 3 w^{3} (4 w^{4}) + 5 (4 w^{4})$

Step 2.2

Rewrite using the commutative property of multiplication.

$10 \cdot 4 w^{5} w^{4} - 3 \cdot 4 w^{3} w^{4} + 5 (4 w^{4})$

Step 2.3

Multiply $4$ by $5$ .

$10 \cdot 4 w^{5} w^{4} - 3 \cdot 4 w^{3} w^{4} + 20 w^{4}$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $w^{4}$ .

$10 \cdot 4 (w^{4} w^{5}) - 3 \cdot 4 w^{3} w^{4} + 20 w^{4}$

Step 3.1.2

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

$10 \cdot 4 w^{4 + 5} - 3 \cdot 4 w^{3} w^{4} + 20 w^{4}$

Step 3.1.3

Add $4$ and $5$ .

$10 \cdot 4 w^{9} - 3 \cdot 4 w^{3} w^{4} + 20 w^{4}$

Step 3.2

Multiply $10$ by $4$ .

$40 w^{9} - 3 \cdot 4 w^{3} w^{4} + 20 w^{4}$

Step 3.3

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

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Step 3.3.1

Move $w^{4}$ .

$40 w^{9} - 3 \cdot 4 (w^{4} w^{3}) + 20 w^{4}$

Step 3.3.2

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

$40 w^{9} - 3 \cdot 4 w^{4 + 3} + 20 w^{4}$

Step 3.3.3

Add $4$ and $3$ .

$40 w^{9} - 3 \cdot 4 w^{7} + 20 w^{4}$

Step 3.4

Multiply $- 3$ by $4$ .

$40 w^{9} - 12 w^{7} + 20 w^{4}$