Algebra Examples

$(3 x^{5} - 9) - (11 + 13 x^{2} - x^{4}) - (10 x^{2} + x^{4})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$3 x^{5} - 9 - 1 \cdot 11 - (13 x^{2}) - - x^{4} - (10 x^{2} + x^{4})$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- 1$ by $11$ .

$3 x^{5} - 9 - 11 - (13 x^{2}) - - x^{4} - (10 x^{2} + x^{4})$

Step 1.2.2

Multiply $13$ by $- 1$ .

$3 x^{5} - 9 - 11 - 13 x^{2} - - x^{4} - (10 x^{2} + x^{4})$

Step 1.2.3

Multiply $- - x^{4}$ .

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Step 1.2.3.1

Multiply $- 1$ by $- 1$ .

$3 x^{5} - 9 - 11 - 13 x^{2} + 1 x^{4} - (10 x^{2} + x^{4})$

Step 1.2.3.2

Multiply $x^{4}$ by $1$ .

$3 x^{5} - 9 - 11 - 13 x^{2} + x^{4} - (10 x^{2} + x^{4})$

Step 1.3

Apply the distributive property.

$3 x^{5} - 9 - 11 - 13 x^{2} + x^{4} - (10 x^{2}) - x^{4}$

Step 1.4

Multiply $10$ by $- 1$ .

$3 x^{5} - 9 - 11 - 13 x^{2} + x^{4} - 10 x^{2} - x^{4}$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $3 x^{5} - 9 - 11 - 13 x^{2} + x^{4} - 10 x^{2} - x^{4}$ .

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Step 2.1.1

Subtract $x^{4}$ from $x^{4}$ .

$3 x^{5} - 9 - 11 - 13 x^{2} - 10 x^{2} + 0$

Step 2.1.2

Add $3 x^{5} - 9 - 11 - 13 x^{2} - 10 x^{2}$ and $0$ .

$3 x^{5} - 9 - 11 - 13 x^{2} - 10 x^{2}$

Step 2.2

Subtract $11$ from $- 9$ .

$3 x^{5} - 20 - 13 x^{2} - 10 x^{2}$

Step 2.3

Subtract $10 x^{2}$ from $- 13 x^{2}$ .

$3 x^{5} - 20 - 23 x^{2}$