Algebra Examples

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

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.

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

Step 2.2

Simplify.

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Step 2.2.1

Multiply $3$ by $- 1$ .

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

Step 2.2.2

Multiply $- 1$ by $- 3$ .

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

Step 2.2.3

Multiply $8$ by $- 1$ .

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

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $3 x^{3}$ from $8 x^{3}$ .

$5 x^{3} - 6 x^{4} + 3 + 3 - 8 x^{4}$

Step 3.2

Subtract $8 x^{4}$ from $- 6 x^{4}$ .

$5 x^{3} - 14 x^{4} + 3 + 3$

Step 3.3

Simplify the expression.

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Step 3.3.1

Add $3$ and $3$ .

$5 x^{3} - 14 x^{4} + 6$

Step 3.3.2

Reorder $5 x^{3}$ and $- 14 x^{4}$ .

$- 14 x^{4} + 5 x^{3} + 6$