Algebra Examples

$(x^{4} - 1) - (- 2 x^{3} - 9 x^{2} + 4 - 11 x^{4} - 6 x)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$x^{4} - 1 - (- 2 x^{3}) - (- 9 x^{2}) - 1 \cdot 4 - (- 11 x^{4}) - (- 6 x)$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- 2$ by $- 1$ .

$x^{4} - 1 + 2 x^{3} - (- 9 x^{2}) - 1 \cdot 4 - (- 11 x^{4}) - (- 6 x)$

Step 1.2.2

Multiply $- 9$ by $- 1$ .

$x^{4} - 1 + 2 x^{3} + 9 x^{2} - 1 \cdot 4 - (- 11 x^{4}) - (- 6 x)$

Step 1.2.3

Multiply $- 1$ by $4$ .

$x^{4} - 1 + 2 x^{3} + 9 x^{2} - 4 - (- 11 x^{4}) - (- 6 x)$

Step 1.2.4

Multiply $- 11$ by $- 1$ .

$x^{4} - 1 + 2 x^{3} + 9 x^{2} - 4 + 11 x^{4} - (- 6 x)$

Step 1.2.5

Multiply $- 6$ by $- 1$ .

$x^{4} - 1 + 2 x^{3} + 9 x^{2} - 4 + 11 x^{4} + 6 x$

Step 2

Simplify by adding terms.

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Step 2.1

Add $x^{4}$ and $11 x^{4}$ .

$12 x^{4} - 1 + 2 x^{3} + 9 x^{2} - 4 + 6 x$

Step 2.2

Subtract $4$ from $- 1$ .

$12 x^{4} + 2 x^{3} + 9 x^{2} - 5 + 6 x$