Finite Math Examples

$(4 x^{5}) (5 - x^{9}) (2 x^{3})$

Step 1

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

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Step 1.1

Move $x^{3}$ .

$4 (x^{3} x^{5}) (5 - x^{9}) \cdot 2$

Step 1.2

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

$4 x^{3 + 5} (5 - x^{9}) \cdot 2$

Step 1.3

Add $3$ and $5$ .

$4 x^{8} (5 - x^{9}) \cdot 2$

Step 2

Simplify by multiplying through.

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Step 2.1

Apply the distributive property.

$(4 x^{8} \cdot 5 + 4 x^{8} (- x^{9})) \cdot 2$

Step 2.2

Simplify the expression.

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Step 2.2.1

Multiply $5$ by $4$ .

$(20 x^{8} + 4 x^{8} (- x^{9})) \cdot 2$

Step 2.2.2

Rewrite using the commutative property of multiplication.

$(20 x^{8} + 4 \cdot - 1 x^{8} x^{9}) \cdot 2$

Step 3

Simplify each term.

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Step 3.1

Multiply $x^{8}$ by $x^{9}$ by adding the exponents.

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Step 3.1.1

Move $x^{9}$ .

$(20 x^{8} + 4 \cdot - 1 (x^{9} x^{8})) \cdot 2$

Step 3.1.2

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

$(20 x^{8} + 4 \cdot - 1 x^{9 + 8}) \cdot 2$

Step 3.1.3

Add $9$ and $8$ .

$(20 x^{8} + 4 \cdot - 1 x^{17}) \cdot 2$

Step 3.2

Multiply $4$ by $- 1$ .

$(20 x^{8} - 4 x^{17}) \cdot 2$

Step 4

Simplify by multiplying through.

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Step 4.1

Apply the distributive property.

$20 x^{8} \cdot 2 - 4 x^{17} \cdot 2$

Step 4.2

Multiply.

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Step 4.2.1

Multiply $2$ by $20$ .

$40 x^{8} - 4 x^{17} \cdot 2$

Step 4.2.2

Multiply $2$ by $- 4$ .

$40 x^{8} - 8 x^{17}$