factor 4x^{2}-28x+49

The given expression is a quadratic trinomial, which can be factored using the following steps:

1. Look for common factors, if any. In this case, there are no common factors among the coefficients.

2. The expression is of the form ax^2 + bx + c, where a = 4, b = -28, and c = 49.

3. To factor the expression, we need to find two numbers that multiply to a*c (4*49 = 196) and add up to b (-28). The two numbers are -14 and -14.

4. Rewrite the middle term (-28x) using the two numbers found in the previous step:
4x^2 - 14x - 14x + 49

5. Factor by grouping:
(4x^2 - 14x) + (-14x + 49)
2x(2x - 7) - 7(2x - 7)

6. Factor out the common binomial factor:
(2x - 7)(2x - 7)

Therefore, the factored form of 4x^2 - 28x + 49 is (2x - 7)^2