Algebra Examples

$(- 2 x^{4} - 5 + 4 x + 2 x^{3}) - (2 x^{3} - 8 x^{4} - 4 x + 8)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- 2 x^{4} - 5 + 4 x + 2 x^{3} - (2 x^{3}) - (- 8 x^{4}) - (- 4 x) - 1 \cdot 8$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $2$ by $- 1$ .

$- 2 x^{4} - 5 + 4 x + 2 x^{3} - 2 x^{3} - (- 8 x^{4}) - (- 4 x) - 1 \cdot 8$

Step 1.2.2

Multiply $- 8$ by $- 1$ .

$- 2 x^{4} - 5 + 4 x + 2 x^{3} - 2 x^{3} + 8 x^{4} - (- 4 x) - 1 \cdot 8$

Step 1.2.3

Multiply $- 4$ by $- 1$ .

$- 2 x^{4} - 5 + 4 x + 2 x^{3} - 2 x^{3} + 8 x^{4} + 4 x - 1 \cdot 8$

Step 1.2.4

Multiply $- 1$ by $8$ .

$- 2 x^{4} - 5 + 4 x + 2 x^{3} - 2 x^{3} + 8 x^{4} + 4 x - 8$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $- 2 x^{4} - 5 + 4 x + 2 x^{3} - 2 x^{3} + 8 x^{4} + 4 x - 8$ .

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Step 2.1.1

Subtract $2 x^{3}$ from $2 x^{3}$ .

$- 2 x^{4} - 5 + 4 x + 0 + 8 x^{4} + 4 x - 8$

Step 2.1.2

Add $- 2 x^{4} - 5 + 4 x$ and $0$ .

$- 2 x^{4} - 5 + 4 x + 8 x^{4} + 4 x - 8$

Step 2.2

Add $- 2 x^{4}$ and $8 x^{4}$ .

$6 x^{4} - 5 + 4 x + 4 x - 8$

Step 2.3

Subtract $8$ from $- 5$ .

$6 x^{4} + 4 x + 4 x - 13$

Step 2.4

Add $4 x$ and $4 x$ .

$6 x^{4} + 8 x - 13$