Evaluate the expression: (5-a)(5-a) - a(a-4) when a = 1/4

The problem is to evaluate the expression:

(5-a)(5-a) - a(a-4)

Given that: a = 1/4

Step-by-step solution:

1. Step 1: Expand the first term (5-a)(5-a).
   This is a square of a binomial: (x-y)² = x² - 2xy + y².
   So, (5-a)² = 5² - 2(5)(a) + a² = 25 - 10a + a².
2. Step 2: Expand the second term a(a-4).
   Distribute 'a' to both terms inside the parenthesis:
   a(a-4) = a * a - a * 4 = a² - 4a.
3. Step 3: Substitute the expanded terms back into the original expression.
   The expression becomes: (25 - 10a + a²) - (a² - 4a).
4. Step 4: Simplify the expression by removing the parenthesis. Remember to change the sign of each term inside the second parenthesis because of the minus sign in front of it.
   25 - 10a + a² - a² + 4a.
5. Step 5: Combine like terms.
   Combine the 'a²' terms: a² - a² = 0.
   Combine the 'a' terms: -10a + 4a = -6a.
   The constant term is 25.
   The simplified expression is: 25 - 6a.
6. Step 6: Substitute the given value of 'a' into the simplified expression.
   Given a = 1/4.
   25 - 6 * (1/4).
7. Step 7: Perform the multiplication.
   6 * (1/4) = 6/4 = 3/2.
8. Step 8: Perform the subtraction.
   25 - 3/2.
   To subtract these, find a common denominator, which is 2.
   25 can be written as 50/2.
   So, 50/2 - 3/2 = (50 - 3) / 2 = 47/2.

Answer: The value of the expression is 47/2 or 23.5