Pre-Algebra Examples

$(20 v^{2} - 9 v^{3}) - (7 v^{3} - 10 v^{4} - 14 v^{2})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$20 v^{2} - 9 v^{3} - (7 v^{3}) - (- 10 v^{4}) - (- 14 v^{2})$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $7$ by $- 1$ .

$20 v^{2} - 9 v^{3} - 7 v^{3} - (- 10 v^{4}) - (- 14 v^{2})$

Step 1.2.2

Multiply $- 10$ by $- 1$ .

$20 v^{2} - 9 v^{3} - 7 v^{3} + 10 v^{4} - (- 14 v^{2})$

Step 1.2.3

Multiply $- 14$ by $- 1$ .

$20 v^{2} - 9 v^{3} - 7 v^{3} + 10 v^{4} + 14 v^{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $20 v^{2}$ and $14 v^{2}$ .

$- 9 v^{3} - 7 v^{3} + 10 v^{4} + 34 v^{2}$

Step 2.2

Subtract $7 v^{3}$ from $- 9 v^{3}$ .

$- 16 v^{3} + 10 v^{4} + 34 v^{2}$

Step 2.3

Reorder $- 16 v^{3}$ and $10 v^{4}$ .

$10 v^{4} - 16 v^{3} + 34 v^{2}$