Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- - x^{3}$ .

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Step 1.2.1.1

Multiply $- 1$ by $- 1$ .

$x^{4} + x^{3} + x^{2} + x - x^{4} + 1 x^{3} - x^{2} - - x$

Step 1.2.1.2

Multiply $x^{3}$ by $1$ .

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

Step 1.2.2

Multiply $- - x$ .

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Step 1.2.2.1

Multiply $- 1$ by $- 1$ .

$x^{4} + x^{3} + x^{2} + x - x^{4} + x^{3} - x^{2} + 1 x$

Step 1.2.2.2

Multiply $x$ by $1$ .

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

Step 2

Simplify by adding terms.

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Step 2.1

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

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Step 2.1.1

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

$x^{3} + x^{2} + x + 0 + x^{3} - x^{2} + x$

Step 2.1.2

Add $x^{3} + x^{2} + x$ and $0$ .

$x^{3} + x^{2} + x + x^{3} - x^{2} + x$

Step 2.1.3

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

$x^{3} + x + x^{3} + 0 + x$

Step 2.1.4

Add $x^{3} + x + x^{3}$ and $0$ .

$x^{3} + x + x^{3} + x$

Step 2.2

Add $x^{3}$ and $x^{3}$ .

$2 x^{3} + x + x$

Step 2.3

Add $x$ and $x$ .

$2 x^{3} + 2 x$