Basic Math Examples

(9 w^{4} - 10 w^{3} + 5) \cdot (8 w^{2})

$(9 w^{4} - 10 w^{3} + 5) \cdot (8 w^{2})$

Step 1

Apply the distributive property.

9 w^{4} (8 w^{2}) - 10 w^{3} (8 w^{2}) + 5 (8 w^{2})

$9 w^{4} (8 w^{2}) - 10 w^{3} (8 w^{2}) + 5 (8 w^{2})$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

9 \cdot 8 w^{4} w^{2} - 10 w^{3} (8 w^{2}) + 5 (8 w^{2})

$9 \cdot 8 w^{4} w^{2} - 10 w^{3} (8 w^{2}) + 5 (8 w^{2})$

Step 2.2

Rewrite using the commutative property of multiplication.

9 \cdot 8 w^{4} w^{2} - 10 \cdot 8 w^{3} w^{2} + 5 (8 w^{2})

$9 \cdot 8 w^{4} w^{2} - 10 \cdot 8 w^{3} w^{2} + 5 (8 w^{2})$

Step 2.3

Multiply

8

$8$ by

5

$5$ .

9 \cdot 8 w^{4} w^{2} - 10 \cdot 8 w^{3} w^{2} + 40 w^{2}

$9 \cdot 8 w^{4} w^{2} - 10 \cdot 8 w^{3} w^{2} + 40 w^{2}$

9 \cdot 8 w^{4} w^{2} - 10 \cdot 8 w^{3} w^{2} + 40 w^{2}

$9 \cdot 8 w^{4} w^{2} - 10 \cdot 8 w^{3} w^{2} + 40 w^{2}$

Step 3

Simplify each term.

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Step 3.1

Multiply

w^{4}

$w^{4}$ by

w^{2}

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

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Step 3.1.1

Move

w^{2}

$w^{2}$ .

9 \cdot 8 (w^{2} w^{4}) - 10 \cdot 8 w^{3} w^{2} + 40 w^{2}

$9 \cdot 8 (w^{2} w^{4}) - 10 \cdot 8 w^{3} w^{2} + 40 w^{2}$

Step 3.1.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$9 \cdot 8 w^{2 + 4} - 10 \cdot 8 w^{3} w^{2} + 40 w^{2}$

Step 3.1.3

Add

$2$ and

$4$ .

$9 \cdot 8 w^{6} - 10 \cdot 8 w^{3} w^{2} + 40 w^{2}$

Step 3.2

Multiply

$9$ by

$8$ .

$72 w^{6} - 10 \cdot 8 w^{3} w^{2} + 40 w^{2}$

Step 3.3

Multiply

$w^{3}$ by

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

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Step 3.3.1

Move

$w^{2}$ .

$72 w^{6} - 10 \cdot 8 (w^{2} w^{3}) + 40 w^{2}$

Step 3.3.2

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$72 w^{6} - 10 \cdot 8 w^{2 + 3} + 40 w^{2}$

Step 3.3.3

Add

$2$ and

$3$ .

$72 w^{6} - 10 \cdot 8 w^{5} + 40 w^{2}$

Step 3.4

Multiply

$- 10$ by

$8$ .

$72 w^{6} - 80 w^{5} + 40 w^{2}$