Algebra Examples

$(- 7 a^{4} - a + 4 a^{2}) - (- 8 a^{2} + a - 7 a^{4})$

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.

$- 7 a^{4} - a + 4 a^{2} - (- 8 a^{2}) - a - (- 7 a^{4})$

Step 2.2

Simplify.

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Step 2.2.1

Multiply $- 8$ by $- 1$ .

$- 7 a^{4} - a + 4 a^{2} + 8 a^{2} - a - (- 7 a^{4})$

Step 2.2.2

Multiply $- 7$ by $- 1$ .

$- 7 a^{4} - a + 4 a^{2} + 8 a^{2} - a + 7 a^{4}$

Step 3

Simplify by adding terms.

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Step 3.1

Combine the opposite terms in $- 7 a^{4} - a + 4 a^{2} + 8 a^{2} - a + 7 a^{4}$ .

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Step 3.1.1

Add $- 7 a^{4}$ and $7 a^{4}$ .

$- a + 4 a^{2} + 8 a^{2} - a + 0$

Step 3.1.2

Add $- a + 4 a^{2} + 8 a^{2} - a$ and $0$ .

$- a + 4 a^{2} + 8 a^{2} - a$

Step 3.2

Subtract $a$ from $- a$ .

$4 a^{2} + 8 a^{2} - 2 a$

Step 3.3

Add $4 a^{2}$ and $8 a^{2}$ .

$12 a^{2} - 2 a$