Algebra Examples

$(2 x^{3} + 4 x^{2} - 5) - (4 x^{3} - x^{2} + 3 x + 12)$

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.

$2 x^{3} + 4 x^{2} - 5 - (4 x^{3}) - - x^{2} - (3 x) - 1 \cdot 12$

Step 2.2

Simplify.

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Step 2.2.1

Multiply $4$ by $- 1$ .

$2 x^{3} + 4 x^{2} - 5 - 4 x^{3} - - x^{2} - (3 x) - 1 \cdot 12$

Step 2.2.2

Multiply $- - x^{2}$ .

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Step 2.2.2.1

Multiply $- 1$ by $- 1$ .

$2 x^{3} + 4 x^{2} - 5 - 4 x^{3} + 1 x^{2} - (3 x) - 1 \cdot 12$

Step 2.2.2.2

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

$2 x^{3} + 4 x^{2} - 5 - 4 x^{3} + x^{2} - (3 x) - 1 \cdot 12$

Step 2.2.3

Multiply $3$ by $- 1$ .

$2 x^{3} + 4 x^{2} - 5 - 4 x^{3} + x^{2} - 3 x - 1 \cdot 12$

Step 2.2.4

Multiply $- 1$ by $12$ .

$2 x^{3} + 4 x^{2} - 5 - 4 x^{3} + x^{2} - 3 x - 12$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $4 x^{3}$ from $2 x^{3}$ .

$- 2 x^{3} + 4 x^{2} - 5 + x^{2} - 3 x - 12$

Step 3.2

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

$- 2 x^{3} + 5 x^{2} - 5 - 3 x - 12$

Step 3.3

Subtract $12$ from $- 5$ .

$- 2 x^{3} + 5 x^{2} - 3 x - 17$