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solve: (a^(2) + b^(2) + 2ab) - (a^(2) + ...

solve: `(a^(2) + b^(2) + 2ab) - (a^(2) + b^(2) - 2ab)`

A

6ab

B

5ab

C

4ab

D

3ab

Text Solution

AI Generated Solution

The correct Answer is:
To solve the expression \((a^{2} + b^{2} + 2ab) - (a^{2} + b^{2} - 2ab)\), we will follow these steps: ### Step 1: Write the expression clearly We start with the expression: \[ (a^{2} + b^{2} + 2ab) - (a^{2} + b^{2} - 2ab) \] ### Step 2: Distribute the negative sign Next, we distribute the negative sign across the second set of parentheses: \[ = a^{2} + b^{2} + 2ab - a^{2} - b^{2} + 2ab \] ### Step 3: Combine like terms Now, we will combine the like terms: - The \(a^{2}\) terms: \(a^{2} - a^{2} = 0\) - The \(b^{2}\) terms: \(b^{2} - b^{2} = 0\) - The \(2ab\) terms: \(2ab + 2ab = 4ab\) Putting it all together, we have: \[ 0 + 0 + 4ab = 4ab \] ### Final Answer Thus, the simplified form of the expression is: \[ \boxed{4ab} \]
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