Factories:
`(l +m)^(2) - 4 lm`

Options

A. `(l+m-2lm)(l+m+2lm)`
B. `(l+m)^(2)`
C. `(l-m)^(2)`
D. none of these

Answer

To factor the expression \((l + m)^{2} - 4lm\), we can follow these steps:

### Step 1: Expand the square
Start by expanding \((l + m)^{2}\):
\[ (l + m)^{2} = l^{2} + 2lm + m^{2} \]

### Step 2: Substitute the expansion into the expression
Now, substitute the expansion back into the original expression:
\[ l^{2} + 2lm + m^{2} - 4lm \]

### Step 3: Combine like terms
Combine the like terms in the expression:
\[ l^{2} + 2lm - 4lm + m^{2} = l^{2} - 2lm + m^{2} \]

### Step 4: Recognize the perfect square
Notice that the expression \(l^{2} - 2lm + m^{2}\) is a perfect square:
\[ l^{2} - 2lm + m^{2} = (l - m)^{2} \]

### Final Answer
Thus, the factorization of the original expression \((l + m)^{2} - 4lm\) is:
\[ (l - m)^{2} \]

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