Algebra Examples

(12 x^{5} + 10 x^{3} - 8 x^{4} - 6 x + 4) - (7 x^{5} + 2 x^{4} - 12 + 6 x - 5 x^{3} + x^{2})

$(12 x^{5} + 10 x^{3} - 8 x^{4} - 6 x + 4) - (7 x^{5} + 2 x^{4} - 12 + 6 x - 5 x^{3} + x^{2})$

Step 1

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

a x^{2} + b x + c

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

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

12 x^{5} + 10 x^{3} - 8 x^{4} - 6 x + 4 - (7 x^{5}) - (2 x^{4}) - - 12 - (6 x) - (- 5 x^{3}) - x^{2}

$12 x^{5} + 10 x^{3} - 8 x^{4} - 6 x + 4 - (7 x^{5}) - (2 x^{4}) - - 12 - (6 x) - (- 5 x^{3}) - x^{2}$

Step 2.2

Simplify.

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Step 2.2.1

Multiply

7

$7$ by

- 1

$- 1$ .

12 x^{5} + 10 x^{3} - 8 x^{4} - 6 x + 4 - 7 x^{5} - (2 x^{4}) - - 12 - (6 x) - (- 5 x^{3}) - x^{2}

$12 x^{5} + 10 x^{3} - 8 x^{4} - 6 x + 4 - 7 x^{5} - (2 x^{4}) - - 12 - (6 x) - (- 5 x^{3}) - x^{2}$

Step 2.2.2

Multiply

2

$2$ by

- 1

$- 1$ .

12 x^{5} + 10 x^{3} - 8 x^{4} - 6 x + 4 - 7 x^{5} - 2 x^{4} - - 12 - (6 x) - (- 5 x^{3}) - x^{2}

$12 x^{5} + 10 x^{3} - 8 x^{4} - 6 x + 4 - 7 x^{5} - 2 x^{4} - - 12 - (6 x) - (- 5 x^{3}) - x^{2}$

Step 2.2.3

Multiply

- 1

$- 1$ by

- 12

$- 12$ .

12 x^{5} + 10 x^{3} - 8 x^{4} - 6 x + 4 - 7 x^{5} - 2 x^{4} + 12 - (6 x) - (- 5 x^{3}) - x^{2}

$12 x^{5} + 10 x^{3} - 8 x^{4} - 6 x + 4 - 7 x^{5} - 2 x^{4} + 12 - (6 x) - (- 5 x^{3}) - x^{2}$

Step 2.2.4

Multiply

6

$6$ by

- 1

$- 1$ .

12 x^{5} + 10 x^{3} - 8 x^{4} - 6 x + 4 - 7 x^{5} - 2 x^{4} + 12 - 6 x - (- 5 x^{3}) - x^{2}

$12 x^{5} + 10 x^{3} - 8 x^{4} - 6 x + 4 - 7 x^{5} - 2 x^{4} + 12 - 6 x - (- 5 x^{3}) - x^{2}$

Step 2.2.5

Multiply

- 5

$- 5$ by

- 1

$- 1$ .

12 x^{5} + 10 x^{3} - 8 x^{4} - 6 x + 4 - 7 x^{5} - 2 x^{4} + 12 - 6 x + 5 x^{3} - x^{2}

$12 x^{5} + 10 x^{3} - 8 x^{4} - 6 x + 4 - 7 x^{5} - 2 x^{4} + 12 - 6 x + 5 x^{3} - x^{2}$

12 x^{5} + 10 x^{3} - 8 x^{4} - 6 x + 4 - 7 x^{5} - 2 x^{4} + 12 - 6 x + 5 x^{3} - x^{2}

$12 x^{5} + 10 x^{3} - 8 x^{4} - 6 x + 4 - 7 x^{5} - 2 x^{4} + 12 - 6 x + 5 x^{3} - x^{2}$

12 x^{5} + 10 x^{3} - 8 x^{4} - 6 x + 4 - 7 x^{5} - 2 x^{4} + 12 - 6 x + 5 x^{3} - x^{2}

$12 x^{5} + 10 x^{3} - 8 x^{4} - 6 x + 4 - 7 x^{5} - 2 x^{4} + 12 - 6 x + 5 x^{3} - x^{2}$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract

7 x^{5}

$7 x^{5}$ from

12 x^{5}

$12 x^{5}$ .

5 x^{5} + 10 x^{3} - 8 x^{4} - 6 x + 4 - 2 x^{4} + 12 - 6 x + 5 x^{3} - x^{2}

$5 x^{5} + 10 x^{3} - 8 x^{4} - 6 x + 4 - 2 x^{4} + 12 - 6 x + 5 x^{3} - x^{2}$

Step 3.2

Add

$10 x^{3}$ and

$5 x^{3}$ .

$5 x^{5} + 15 x^{3} - 8 x^{4} - 6 x + 4 - 2 x^{4} + 12 - 6 x - x^{2}$

Step 3.3

Subtract

$2 x^{4}$ from

$- 8 x^{4}$ .

$5 x^{5} + 15 x^{3} - 10 x^{4} - 6 x + 4 + 12 - 6 x - x^{2}$

Step 3.4

Subtract

$6 x$ from

$- 6 x$ .

$5 x^{5} + 15 x^{3} - 10 x^{4} - 12 x + 4 + 12 - x^{2}$

Step 3.5

Simplify the expression.

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Step 3.5.1

Add

$4$ and

$12$ .

$5 x^{5} + 15 x^{3} - 10 x^{4} - 12 x + 16 - x^{2}$

Step 3.5.2

Move

$16$ .

$5 x^{5} + 15 x^{3} - 10 x^{4} - 12 x - x^{2} + 16$

Step 3.5.3

Move

$- 12 x$ .

$5 x^{5} + 15 x^{3} - 10 x^{4} - x^{2} - 12 x + 16$

Step 3.5.4

Move

$15 x^{3}$ .

$5 x^{5} - 10 x^{4} + 15 x^{3} - x^{2} - 12 x + 16$