Algebra Examples

$(x^{2} - 8) - (3 x^{3} - 6 x - 4 + 9 x^{2})$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$x^{2} - 8 - (3 x^{3}) - (- 6 x) - - 4 - (9 x^{2})$

Step 2.2

Simplify.

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Step 2.2.1

Multiply $3$ by $- 1$ .

$x^{2} - 8 - 3 x^{3} - (- 6 x) - - 4 - (9 x^{2})$

Step 2.2.2

Multiply $- 6$ by $- 1$ .

$x^{2} - 8 - 3 x^{3} + 6 x - - 4 - (9 x^{2})$

Step 2.2.3

Multiply $- 1$ by $- 4$ .

$x^{2} - 8 - 3 x^{3} + 6 x + 4 - (9 x^{2})$

Step 2.2.4

Multiply $9$ by $- 1$ .

$x^{2} - 8 - 3 x^{3} + 6 x + 4 - 9 x^{2}$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $9 x^{2}$ from $x^{2}$ .

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

Step 3.2

Simplify the expression.

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Step 3.2.1

Add $- 8$ and $4$ .

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

Step 3.2.2

Reorder $- 8 x^{2}$ and $- 3 x^{3}$ .

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