Algebra Examples

$(- 3 x^{4} + 6 x^{3} - 11 x^{2} + 5) - (5 x^{4} + 2 x^{3} - x)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- 3 x^{4} + 6 x^{3} - 11 x^{2} + 5 - (5 x^{4}) - (2 x^{3}) - - x$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $5$ by $- 1$ .

$- 3 x^{4} + 6 x^{3} - 11 x^{2} + 5 - 5 x^{4} - (2 x^{3}) - - x$

Step 1.2.2

Multiply $2$ by $- 1$ .

$- 3 x^{4} + 6 x^{3} - 11 x^{2} + 5 - 5 x^{4} - 2 x^{3} - - x$

Step 1.2.3

Multiply $- - x$ .

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Step 1.2.3.1

Multiply $- 1$ by $- 1$ .

$- 3 x^{4} + 6 x^{3} - 11 x^{2} + 5 - 5 x^{4} - 2 x^{3} + 1 x$

Step 1.2.3.2

Multiply $x$ by $1$ .

$- 3 x^{4} + 6 x^{3} - 11 x^{2} + 5 - 5 x^{4} - 2 x^{3} + x$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $5 x^{4}$ from $- 3 x^{4}$ .

$- 8 x^{4} + 6 x^{3} - 11 x^{2} + 5 - 2 x^{3} + x$

Step 2.2

Subtract $2 x^{3}$ from $6 x^{3}$ .

$- 8 x^{4} + 4 x^{3} - 11 x^{2} + 5 + x$

Step 2.3

Move $5$ .

$- 8 x^{4} + 4 x^{3} - 11 x^{2} + x + 5$