Algebra Examples

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

Step 1

Remove parentheses.

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

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Multiply $2$ by $- 1$ .

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

Step 3

Simplify by adding terms.

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Step 3.1

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

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

Step 3.2

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

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Step 3.2.1

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

$- 3 x^{2} - 2 x^{3} + 0 + x^{3} - 5 x$

Step 3.2.2

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

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

Step 3.3

Add $- 2 x^{3}$ and $x^{3}$ .

$- 3 x^{2} - x^{3} - 5 x$

Step 3.4

Reorder $- 3 x^{2}$ and $- x^{3}$ .

$- x^{3} - 3 x^{2} - 5 x$