Algebra Examples

$(x^{3} + 6 x^{2} - 17 x + 2) - (x^{3} - x^{2} - 11 x + 36)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$x^{3} + 6 x^{2} - 17 x + 2 - x^{3} - - x^{2} - (- 11 x) - 1 \cdot 36$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- - x^{2}$ .

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Step 1.2.1.1

Multiply $- 1$ by $- 1$ .

$x^{3} + 6 x^{2} - 17 x + 2 - x^{3} + 1 x^{2} - (- 11 x) - 1 \cdot 36$

Step 1.2.1.2

Multiply $x^{2}$ by $1$ .

$x^{3} + 6 x^{2} - 17 x + 2 - x^{3} + x^{2} - (- 11 x) - 1 \cdot 36$

Step 1.2.2

Multiply $- 11$ by $- 1$ .

$x^{3} + 6 x^{2} - 17 x + 2 - x^{3} + x^{2} + 11 x - 1 \cdot 36$

Step 1.2.3

Multiply $- 1$ by $36$ .

$x^{3} + 6 x^{2} - 17 x + 2 - x^{3} + x^{2} + 11 x - 36$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $x^{3} + 6 x^{2} - 17 x + 2 - x^{3} + x^{2} + 11 x - 36$ .

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Step 2.1.1

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

$6 x^{2} - 17 x + 2 + 0 + x^{2} + 11 x - 36$

Step 2.1.2

Add $6 x^{2} - 17 x + 2$ and $0$ .

$6 x^{2} - 17 x + 2 + x^{2} + 11 x - 36$

Step 2.2

Add $6 x^{2}$ and $x^{2}$ .

$7 x^{2} - 17 x + 2 + 11 x - 36$

Step 2.3

Add $- 17 x$ and $11 x$ .

$7 x^{2} - 6 x + 2 - 36$

Step 2.4

Subtract $36$ from $2$ .

$7 x^{2} - 6 x - 34$