Algebra Examples

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

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Simplify.

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Step 2.2.1

Multiply $5$ by $- 1$ .

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

Step 2.2.2

Multiply $4$ by $- 1$ .

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

Step 2.3

Remove parentheses.

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

Step 3

Simplify by adding terms.

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Step 3.1

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

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Step 3.1.1

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

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

Step 3.1.2

Add $5 u^{2} v + 4 u v^{2}$ and $0$ .

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

Step 3.2

Simplify the expression.

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Step 3.2.1

Move $4 u v^{2}$ .

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

Step 3.2.2

Reorder $5 u^{2} v$ and $- 5 u^{2} v^{2}$ .

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