Find `(x+y)^(2) - (x-y)^(2)` ?
A. `2x^(2)y^(2)`
B. `4xy`
C. `2x^(2)+2y^(2)`
D. `x^(2)-y^(2)+2xy`

Options

A. C
B. D
C. A
D. B

Answer

To solve the expression \((x+y)^{2} - (x-y)^{2}\), we can use the algebraic identities for the squares of binomials.

### Step 1: Apply the binomial square formulas
We know the following formulas:
- \((x+y)^{2} = x^{2} + y^{2} + 2xy\)
- \((x-y)^{2} = x^{2} + y^{2} - 2xy\)

### Step 2: Substitute the formulas into the expression
Now, we can substitute these formulas into the expression:
\[ (x+y)^{2} - (x-y)^{2} = (x^{2} + y^{2} + 2xy) - (x^{2} + y^{2} - 2xy) \]

### Step 3: Distribute the negative sign
Next, we distribute the negative sign across the second part of the expression:
\[ = x^{2} + y^{2} + 2xy - x^{2} - y^{2} + 2xy \]

### Step 4: Combine like terms
Now, we can combine like terms:
- The \(x^{2}\) terms: \(x^{2} - x^{2} = 0\)
- The \(y^{2}\) terms: \(y^{2} - y^{2} = 0\)
- The \(2xy\) terms: \(2xy + 2xy = 4xy\)

Thus, we have:
\[ = 0 + 0 + 4xy = 4xy \]

### Final Answer
Therefore, the final answer is:
\[ \boxed{4xy} \]