Linear Algebra Examples

$(3 v^{5} + 8 v^{3} - 10 v^{2}) - (- 12 v^{5} + 4 v^{3} + 14 v^{2})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$3 v^{5} + 8 v^{3} - 10 v^{2} - (- 12 v^{5}) - (4 v^{3}) - (14 v^{2})$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- 12$ by $- 1$ .

$3 v^{5} + 8 v^{3} - 10 v^{2} + 12 v^{5} - (4 v^{3}) - (14 v^{2})$

Step 1.2.2

Multiply $4$ by $- 1$ .

$3 v^{5} + 8 v^{3} - 10 v^{2} + 12 v^{5} - 4 v^{3} - (14 v^{2})$

Step 1.2.3

Multiply $14$ by $- 1$ .

$3 v^{5} + 8 v^{3} - 10 v^{2} + 12 v^{5} - 4 v^{3} - 14 v^{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $3 v^{5}$ and $12 v^{5}$ .

$15 v^{5} + 8 v^{3} - 10 v^{2} - 4 v^{3} - 14 v^{2}$

Step 2.2

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

$15 v^{5} + 4 v^{3} - 10 v^{2} - 14 v^{2}$

Step 2.3

Subtract $14 v^{2}$ from $- 10 v^{2}$ .

$15 v^{5} + 4 v^{3} - 24 v^{2}$