To factor the expression 49x^2 - 28xy + 0.4y^2, we can use the concept of factoring quadratic expressions.

Step 1: Identify the common factors, if any.
In this case, we can see that all the terms have a common factor of 0.4.

Step 2: Divide each term by the common factor.
Dividing all the terms by 0.4, we get:
49x^2/0.4 - 28xy/0.4 + 0.4y^2/0.4
This simplifies to:
122.5x^2 - 70xy + y^2

Step 3: Factor the quadratic expression.
To factor the quadratic expression, we need to find two binomials that, when multiplied, give us the original expression. These binomials will have the form (ax + by)(cx + dy), where a, b, c, and d are constants.

In this case, the expression is 122.5x^2 - 70xy + y^2. We can see that the leading coefficient is not a perfect square, so we cannot use the shortcut method.

To factor this expression, we need to find two numbers that multiply to give us 122.5 and add up to -70. Since 122.5 is not a perfect square, we need to find two decimal numbers that satisfy this condition.

After some trial and error, we find that -35 and -35.5 are suitable numbers. So we can rewrite the expression as:
(35x - 35.5y)(35x - 35.5y)

Step 4: Simplify the expression.
Since both binomials are identical, we can write the final factored form as:
(35x - 35.5y)^2

Therefore, the correct answer is option (c) (7x - 2y)^2.