Algebra Examples

$(2 x^{4} + x^{3} - 3 x + 8) - (x^{4} - x^{3} - 6 x^{2} + 7 x)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$2 x^{4} + x^{3} - 3 x + 8 - x^{4} - - x^{3} - (- 6 x^{2}) - (7 x)$

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 $- 1$ .

$2 x^{4} + x^{3} - 3 x + 8 - x^{4} + 1 x^{3} - (- 6 x^{2}) - (7 x)$

Step 1.2.1.2

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

$2 x^{4} + x^{3} - 3 x + 8 - x^{4} + x^{3} - (- 6 x^{2}) - (7 x)$

Step 1.2.2

Multiply $- 6$ by $- 1$ .

$2 x^{4} + x^{3} - 3 x + 8 - x^{4} + x^{3} + 6 x^{2} - (7 x)$

Step 1.2.3

Multiply $7$ by $- 1$ .

$2 x^{4} + x^{3} - 3 x + 8 - x^{4} + x^{3} + 6 x^{2} - 7 x$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $x^{4}$ from $2 x^{4}$ .

$x^{4} + x^{3} - 3 x + 8 + x^{3} + 6 x^{2} - 7 x$

Step 2.2

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

$x^{4} + 2 x^{3} - 3 x + 8 + 6 x^{2} - 7 x$

Step 2.3

Subtract $7 x$ from $- 3 x$ .

$x^{4} + 2 x^{3} - 10 x + 8 + 6 x^{2}$