(a-d)²-(a-c)²

To simplify the expression \((a-d)^2 - (a-c)^2\), we can use the difference of squares formula, which states that \(x^2 - y^2 = (x - y)(x + y)\).

Let:

• \(x = (a-d)\)
• \(y = (a-c)\)

Then, the expression can be rewritten as: \[ ((a - d) - (a - c))((a - d) + (a - c)) \]

Now, let's simplify each part:

1. For the first term, \((a - d) - (a - c)\): \[ (a - d) - (a - c) = c - d \]

2. For the second term, \((a - d) + (a - c)\): \[ (a - d) + (a - c) = (a - d + a - c) = 2a - (c + d) \]

Combining these, we find: \[ (a-d)^2 - (a-c)^2 = (c - d)(2a - (c + d)) \]

So, the simplified expression is: \[ (c - d)(2a - (c + d)) \]