Simplify (-6u^2v^4+12uv^4)-(2u^3v^4-9u^2v^4-5uv^4)+(-3u^3v^4-13uv^4)

$(- 6 u^{2} v^{4} + 12 u v^{4}) - (2 u^{3} v^{4} - 9 u^{2} v^{4} - 5 u v^{4}) + (- 3 u^{3} v^{4} - 13 u v^{4})$

Step 1

Remove parentheses.

$(- 6 u^{2} v^{4} + 12 u v^{4}) - (2 u^{3} v^{4} - 9 u^{2} v^{4} - 5 u v^{4}) - 3 u^{3} v^{4} - 13 u v^{4}$

Step 2

Simplify each term.

Apply the distributive property.

$- 6 u^{2} v^{4} + 12 u v^{4} - (2 u^{3} v^{4}) - (- 9 u^{2} v^{4}) - (- 5 u v^{4}) - 3 u^{3} v^{4} - 13 u v^{4}$

Simplify.

Multiply $2$ by $- 1$ .

$- 6 u^{2} v^{4} + 12 u v^{4} - 2 (u^{3} v^{4}) - (- 9 u^{2} v^{4}) - (- 5 u v^{4}) - 3 u^{3} v^{4} - 13 u v^{4}$

Multiply $- 9$ by $- 1$ .

$- 6 u^{2} v^{4} + 12 u v^{4} - 2 (u^{3} v^{4}) + 9 (u^{2} v^{4}) - (- 5 u v^{4}) - 3 u^{3} v^{4} - 13 u v^{4}$

Multiply $- 5$ by $- 1$ .

$- 6 u^{2} v^{4} + 12 u v^{4} - 2 (u^{3} v^{4}) + 9 (u^{2} v^{4}) + 5 (u v^{4}) - 3 u^{3} v^{4} - 13 u v^{4}$

Remove parentheses.

$- 6 u^{2} v^{4} + 12 u v^{4} - 2 u^{3} v^{4} + 9 u^{2} v^{4} + 5 u v^{4} - 3 u^{3} v^{4} - 13 u v^{4}$

Step 3

Simplify by adding terms.

Add $- 6 u^{2} v^{4}$ and $9 u^{2} v^{4}$ .

$3 u^{2} v^{4} + 12 u v^{4} - 2 u^{3} v^{4} + 5 u v^{4} - 3 u^{3} v^{4} - 13 u v^{4}$

Add $12 u v^{4}$ and $5 u v^{4}$ .

$3 u^{2} v^{4} + 17 u v^{4} - 2 u^{3} v^{4} - 3 u^{3} v^{4} - 13 u v^{4}$

Subtract $13 u v^{4}$ from $17 u v^{4}$ .

$3 u^{2} v^{4} + 4 u v^{4} - 2 u^{3} v^{4} - 3 u^{3} v^{4}$

Subtract $3 u^{3} v^{4}$ from $- 2 u^{3} v^{4}$ .

$3 u^{2} v^{4} + 4 u v^{4} - 5 u^{3} v^{4}$