Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Simplify.

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Step 1.2.1

Multiply $4$ by $- 1$ .

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

Step 1.2.2

Multiply $5$ by $- 1$ .

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

Step 1.2.3

Multiply $- 5$ by $- 1$ .

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

Step 1.3

Remove parentheses.

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

Step 2

Combine the opposite terms in $6 u^{2} + 5 u^{2} v^{2} - 3 u v^{2} - 4 u^{4} - 5 u^{2} v^{2} + 5 u v$ .

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Step 2.1

Subtract $5 u^{2} v^{2}$ from $5 u^{2} v^{2}$ .

$6 u^{2} - 3 u v^{2} - 4 u^{4} + 0 + 5 u v$

Step 2.2

Add $6 u^{2} - 3 u v^{2} - 4 u^{4}$ and $0$ .

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