Algebra Examples

$(5 x^{4} + 13 x^{2} - x + 10) - (- 6 x^{4} + 9 x^{3} + 7)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$5 x^{4} + 13 x^{2} - x + 10 - (- 6 x^{4}) - (9 x^{3}) - 1 \cdot 7$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- 6$ by $- 1$ .

$5 x^{4} + 13 x^{2} - x + 10 + 6 x^{4} - (9 x^{3}) - 1 \cdot 7$

Step 1.2.2

Multiply $9$ by $- 1$ .

$5 x^{4} + 13 x^{2} - x + 10 + 6 x^{4} - 9 x^{3} - 1 \cdot 7$

Step 1.2.3

Multiply $- 1$ by $7$ .

$5 x^{4} + 13 x^{2} - x + 10 + 6 x^{4} - 9 x^{3} - 7$

Step 2

Simplify by adding terms.

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Step 2.1

Add $5 x^{4}$ and $6 x^{4}$ .

$11 x^{4} + 13 x^{2} - x + 10 - 9 x^{3} - 7$

Step 2.2

Simplify the expression.

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Step 2.2.1

Subtract $7$ from $10$ .

$11 x^{4} + 13 x^{2} - x - 9 x^{3} + 3$

Step 2.2.2

Move $- x$ .

$11 x^{4} + 13 x^{2} - 9 x^{3} - x + 3$

Step 2.2.3

Move $13 x^{2}$ .

$11 x^{4} - 9 x^{3} + 13 x^{2} - x + 3$