Algebra Examples

$(5 x^{3} + 2 x - 1 + 4 x^{2}) + (6 - 5 x + x^{3}) - (2 x^{2} + 5)$

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.

$5 x^{3} + 2 x - 1 + 4 x^{2} + 6 - 5 x + x^{3} - (2 x^{2}) - 1 \cdot 5$

Step 2.2

Multiply $2$ by $- 1$ .

$5 x^{3} + 2 x - 1 + 4 x^{2} + 6 - 5 x + x^{3} - 2 x^{2} - 1 \cdot 5$

Step 2.3

Multiply $- 1$ by $5$ .

$5 x^{3} + 2 x - 1 + 4 x^{2} + 6 - 5 x + x^{3} - 2 x^{2} - 5$

Step 3

Simplify by adding terms.

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Step 3.1

Add $5 x^{3}$ and $x^{3}$ .

$6 x^{3} + 2 x - 1 + 4 x^{2} + 6 - 5 x - 2 x^{2} - 5$

Step 3.2

Subtract $5 x$ from $2 x$ .

$6 x^{3} - 3 x - 1 + 4 x^{2} + 6 - 2 x^{2} - 5$

Step 3.3

Add $- 1$ and $6$ .

$6 x^{3} - 3 x + 4 x^{2} + 5 - 2 x^{2} - 5$

Step 3.4

Combine the opposite terms in $6 x^{3} - 3 x + 4 x^{2} + 5 - 2 x^{2} - 5$ .

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Step 3.4.1

Subtract $5$ from $5$ .

$6 x^{3} - 3 x + 4 x^{2} - 2 x^{2} + 0$

Step 3.4.2

Add $6 x^{3} - 3 x + 4 x^{2} - 2 x^{2}$ and $0$ .

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

Step 3.5

Subtract $2 x^{2}$ from $4 x^{2}$ .

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

Step 3.6

Move $- 3 x$ .

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