Algebra Examples

$(12 a^{5} - 6 a - 10 a^{3}) - (10 a - 2 a^{5} - 14 a^{4})$

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.

$12 a^{5} - 6 a - 10 a^{3} - (10 a) - (- 2 a^{5}) - (- 14 a^{4})$

Step 2.2

Simplify.

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Step 2.2.1

Multiply $10$ by $- 1$ .

$12 a^{5} - 6 a - 10 a^{3} - 10 a - (- 2 a^{5}) - (- 14 a^{4})$

Step 2.2.2

Multiply $- 2$ by $- 1$ .

$12 a^{5} - 6 a - 10 a^{3} - 10 a + 2 a^{5} - (- 14 a^{4})$

Step 2.2.3

Multiply $- 14$ by $- 1$ .

$12 a^{5} - 6 a - 10 a^{3} - 10 a + 2 a^{5} + 14 a^{4}$

Step 3

Simplify by adding terms.

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Step 3.1

Add $12 a^{5}$ and $2 a^{5}$ .

$14 a^{5} - 6 a - 10 a^{3} - 10 a + 14 a^{4}$

Step 3.2

Subtract $10 a$ from $- 6 a$ .

$14 a^{5} - 10 a^{3} - 16 a + 14 a^{4}$

Step 3.3

Reorder.

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Step 3.3.1

Move $- 16 a$ .

$14 a^{5} - 10 a^{3} + 14 a^{4} - 16 a$

Step 3.3.2

Move $- 10 a^{3}$ .

$14 a^{5} + 14 a^{4} - 10 a^{3} - 16 a$