Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- 5$ by $- 1$ .

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

Step 1.2.2

Multiply $3$ by $- 1$ .

$3 x^{3} - 4 x^{2} + x - 2 - x^{3} + 5 x^{2} - 3 x - 1 \cdot 2$

Step 1.2.3

Multiply $- 1$ by $2$ .

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

Step 2

Simplify by adding terms.

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Step 2.1

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

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

Step 2.2

Add $- 4 x^{2}$ and $5 x^{2}$ .

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

Step 2.3

Subtract $3 x$ from $x$ .

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

Step 2.4

Subtract $2$ from $- 2$ .

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