Algebra Examples

$(5 v^{2} - 3 v^{4} - 7 v + 6 v^{3}) - (8 v^{4} + 6 + 4 v^{3} - 6 v)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$5 v^{2} - 3 v^{4} - 7 v + 6 v^{3} - (8 v^{4}) - 1 \cdot 6 - (4 v^{3}) - (- 6 v)$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $8$ by $- 1$ .

$5 v^{2} - 3 v^{4} - 7 v + 6 v^{3} - 8 v^{4} - 1 \cdot 6 - (4 v^{3}) - (- 6 v)$

Step 1.2.2

Multiply $- 1$ by $6$ .

$5 v^{2} - 3 v^{4} - 7 v + 6 v^{3} - 8 v^{4} - 6 - (4 v^{3}) - (- 6 v)$

Step 1.2.3

Multiply $4$ by $- 1$ .

$5 v^{2} - 3 v^{4} - 7 v + 6 v^{3} - 8 v^{4} - 6 - 4 v^{3} - (- 6 v)$

Step 1.2.4

Multiply $- 6$ by $- 1$ .

$5 v^{2} - 3 v^{4} - 7 v + 6 v^{3} - 8 v^{4} - 6 - 4 v^{3} + 6 v$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $8 v^{4}$ from $- 3 v^{4}$ .

$5 v^{2} - 11 v^{4} - 7 v + 6 v^{3} - 6 - 4 v^{3} + 6 v$

Step 2.2

Add $- 7 v$ and $6 v$ .

$5 v^{2} - 11 v^{4} + 6 v^{3} - 6 - 4 v^{3} - v$

Step 2.3

Subtract $4 v^{3}$ from $6 v^{3}$ .

$5 v^{2} - 11 v^{4} + 2 v^{3} - 6 - v$

Step 2.4

Reorder.

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Step 2.4.1

Move $- 6$ .

$5 v^{2} - 11 v^{4} + 2 v^{3} - v - 6$

Step 2.4.2

Move $5 v^{2}$ .

$- 11 v^{4} + 2 v^{3} + 5 v^{2} - v - 6$