Fractorise:
`(l+m) ^(2) -(l -m)^(2)`

Answer

To factorize the expression \((l+m)^2 - (l-m)^2\), we can follow these steps:

### Step 1: Recognize the difference of squares
The expression \((l+m)^2 - (l-m)^2\) is in the form of \(a^2 - b^2\), where \(a = (l+m)\) and \(b = (l-m)\). We can use the identity:
\[ a^2 - b^2 = (a+b)(a-b) \]

### Step 2: Apply the identity
Using the identity, we can rewrite the expression:
\[ (l+m)^2 - (l-m)^2 = [(l+m) + (l-m)][(l+m) - (l-m)] \]

### Step 3: Simplify the first bracket
Now, simplify \((l+m) + (l-m)\):
\[ (l+m) + (l-m) = l + m + l - m = 2l \]

### Step 4: Simplify the second bracket
Next, simplify \((l+m) - (l-m)\):
\[ (l+m) - (l-m) = l + m - l + m = 2m \]

### Step 5: Combine the results
Now, substituting back into the expression, we have:
\[ (l+m)^2 - (l-m)^2 = (2l)(2m) \]

### Step 6: Final expression
This simplifies to:
\[ 4lm \]

Thus, the factorized form of \((l+m)^2 - (l-m)^2\) is:
\[ 4lm \]

---