factor 25x^{2}-20x+4

To factor the expression 25x^2 - 20x + 4, we first look for a common factor among all terms. In this case, there is no common factor among the terms.

Next, we need to factor the quadratic trinomial 25x^2 - 20x + 4. To do this, we need to find two numbers that multiply to the product of the leading coefficient (25) and the constant term (4), which is 25*4 = 100, and add up to the middle coefficient (-20).

The two numbers that satisfy these conditions are -10 and -10. Therefore, we can rewrite the trinomial as:

25x^2 - 10x - 10x + 4

Now, we can factor by grouping:

25x^2 - 10x - 10x + 4
= 5x(5x - 2) - 2(5x - 2)
= (5x - 2)(5x - 2)
= (5x - 2)^2

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