Finite Math Examples

$- 10 x^{4} y^{4} (x^{4} - 4 x^{4} y^{4} + 4 y^{3})$

Step 1

Apply the distributive property.

$- 10 x^{4} y^{4} x^{4} - 10 x^{4} y^{4} (- 4 x^{4} y^{4}) - 10 x^{4} y^{4} (4 y^{3})$

Step 2

Simplify.

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Step 2.1

Multiply $x^{4}$ by $x^{4}$ by adding the exponents.

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Step 2.1.1

Move $x^{4}$ .

$- 10 (x^{4} x^{4}) y^{4} - 10 x^{4} y^{4} (- 4 x^{4} y^{4}) - 10 x^{4} y^{4} (4 y^{3})$

Step 2.1.2

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

$- 10 x^{4 + 4} y^{4} - 10 x^{4} y^{4} (- 4 x^{4} y^{4}) - 10 x^{4} y^{4} (4 y^{3})$

Step 2.1.3

Add $4$ and $4$ .

$- 10 x^{8} y^{4} - 10 x^{4} y^{4} (- 4 x^{4} y^{4}) - 10 x^{4} y^{4} (4 y^{3})$

Step 2.2

Multiply $x^{4}$ by $x^{4}$ by adding the exponents.

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Step 2.2.1

Move $x^{4}$ .

$- 10 x^{8} y^{4} - 10 (x^{4} x^{4}) y^{4} (- 4 y^{4}) - 10 x^{4} y^{4} (4 y^{3})$

Step 2.2.2

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

$- 10 x^{8} y^{4} - 10 x^{4 + 4} y^{4} (- 4 y^{4}) - 10 x^{4} y^{4} (4 y^{3})$

Step 2.2.3

Add $4$ and $4$ .

$- 10 x^{8} y^{4} - 10 x^{8} y^{4} (- 4 y^{4}) - 10 x^{4} y^{4} (4 y^{3})$

Step 2.3

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

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Step 2.3.1

Move $y^{3}$ .

$- 10 x^{8} y^{4} - 10 x^{8} y^{4} (- 4 y^{4}) - 10 x^{4} (y^{3} y^{4}) \cdot 4$

Step 2.3.2

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

$- 10 x^{8} y^{4} - 10 x^{8} y^{4} (- 4 y^{4}) - 10 x^{4} y^{3 + 4} \cdot 4$

Step 2.3.3

Add $3$ and $4$ .

$- 10 x^{8} y^{4} - 10 x^{8} y^{4} (- 4 y^{4}) - 10 x^{4} y^{7} \cdot 4$

Step 3

Simplify each term.

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Step 3.1

Multiply $y^{4}$ by $y^{4}$ by adding the exponents.

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Step 3.1.1

Move $y^{4}$ .

$- 10 x^{8} y^{4} - 10 x^{8} (y^{4} y^{4}) \cdot - 4 - 10 x^{4} y^{7} \cdot 4$

Step 3.1.2

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

$- 10 x^{8} y^{4} - 10 x^{8} y^{4 + 4} \cdot - 4 - 10 x^{4} y^{7} \cdot 4$

Step 3.1.3

Add $4$ and $4$ .

$- 10 x^{8} y^{4} - 10 x^{8} y^{8} \cdot - 4 - 10 x^{4} y^{7} \cdot 4$

Step 3.2

Multiply $- 4$ by $- 10$ .

$- 10 x^{8} y^{4} + 40 x^{8} y^{8} - 10 x^{4} y^{7} \cdot 4$

Step 3.3

Multiply $4$ by $- 10$ .

$- 10 x^{8} y^{4} + 40 x^{8} y^{8} - 40 x^{4} y^{7}$