25x^(2)-20x+4

To factor the quadratic expression 25x^2 - 20x + 4, we can use the factoring formula for a quadratic equation of the form ax^2 + bx + c:

The factoring formula is:
ax^2 + bx + c = (mx + p)(nx + q)

Given expression is 25x^2 - 20x + 4, where a = 25, b = -20, and c = 4.

First, find the product 'a*c':
a * c = 25 * 4 = 100

Next, find two numbers that multiply to 100 and add up to -20:
The two numbers are -10 and -10 (since -10 * -10 = 100 and -10 + (-10) = -20)

Now, rewrite the middle term (-20x) using the numbers -10 and -10:
25x^2 - 10x - 10x + 4

Group the terms:
= (25x^2 - 10x) + (-10x + 4)

Factor out the common terms in each group:
= 5x(5x - 2) - 2(5x - 2)

Factor out the common binomial factor:
= (5x - 2)(5x - 2)

Now, write it in simplified form:
= (5x - 2)^2

Therefore, the factored form of 25x^2 - 20x + 4 is (5x - 2)^2.