Algebra Examples

$(7 x^{4} + 11 x^{3} - x^{2} - 8 x + 6) - (- 12 x^{4} + 9 x^{2} - 15)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$7 x^{4} + 11 x^{3} - x^{2} - 8 x + 6 - (- 12 x^{4}) - (9 x^{2}) - - 15$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- 12$ by $- 1$ .

$7 x^{4} + 11 x^{3} - x^{2} - 8 x + 6 + 12 x^{4} - (9 x^{2}) - - 15$

Step 1.2.2

Multiply $9$ by $- 1$ .

$7 x^{4} + 11 x^{3} - x^{2} - 8 x + 6 + 12 x^{4} - 9 x^{2} - - 15$

Step 1.2.3

Multiply $- 1$ by $- 15$ .

$7 x^{4} + 11 x^{3} - x^{2} - 8 x + 6 + 12 x^{4} - 9 x^{2} + 15$

Step 2

Simplify by adding terms.

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Step 2.1

Add $7 x^{4}$ and $12 x^{4}$ .

$19 x^{4} + 11 x^{3} - x^{2} - 8 x + 6 - 9 x^{2} + 15$

Step 2.2

Subtract $9 x^{2}$ from $- x^{2}$ .

$19 x^{4} + 11 x^{3} - 10 x^{2} - 8 x + 6 + 15$

Step 2.3

Add $6$ and $15$ .

$19 x^{4} + 11 x^{3} - 10 x^{2} - 8 x + 21$