The provided image contains a mathematical expression and an equation. The expression is (5-a)(5-a)-a(a-4) and the equation is a = 1/4. Please provide the solution to this problem.

The Problem:

The image shows a mathematical expression: \( (5-a)(5-a)-a(a-4) \) and an equation: \( a = \frac{1}{4} \). The task is to simplify the expression and potentially substitute the value of 'a'.

Simplification of the Expression:

1. Expand the squared term: \( (5-a)(5-a) = (5-a)^2 = 25 - 10a + a^2 \)
2. Distribute the second term: \( -a(a-4) = -a^2 + 4a \)
3. Combine the expanded terms: \( (25 - 10a + a^2) + (-a^2 + 4a) \)
4. Group like terms: \( (a^2 - a^2) + (-10a + 4a) + 25 \)
5. Simplify: \( 0a^2 - 6a + 25 = -6a + 25 \)

Substitution of 'a':

Now, substitute the given value of \( a = \frac{1}{4} \) into the simplified expression:

1. Substitute 'a': \( -6\left(\frac{1}{4}\right) + 25 \)
2. Multiply: \( -\frac{6}{4} + 25 = -\frac{3}{2} + 25 \)
3. Convert to a common denominator: \( -\frac{3}{2} + \frac{50}{2} \)
4. Add: \( \frac{-3 + 50}{2} = \frac{47}{2} \)

Final Answer:

The simplified expression is \( -6a + 25 \). When \( a = \frac{1}{4} \), the value of the expression is \( \frac{47}{2} \) or \( 23.5 \).