Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- - x^{4}$ .

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Step 1.2.1.1

Multiply $- 1$ by $- 1$ .

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

Step 1.2.1.2

Multiply $x^{4}$ by $1$ .

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

Step 1.2.2

Multiply $- 3$ by $- 1$ .

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

Step 2

Simplify by adding terms.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

Add $- 3 x^{5} - x^{3} + 2 x^{2} - x^{5}$ and $0$ .

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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