a^2 - 4ab +4b^2 - 16x^2

(a-2b)^2 - 16x^2

now you have a difference of squares
(a-2b+4x)(a-2b-4x)

Don't have

To simplify the expression a^2 - 4ab + 4b^2 - 16x^2, we can follow these steps:

Step 1: Group the terms with similar variables:
(a^2 - 4ab + 4b^2) - 16x^2

Step 2: Factor the first three terms:
(a - 2b)^2 - 16x^2

Step 3: Recognize that this expression is now in the form of a difference of squares, which can be factored further:
((a - 2b) - 4x)((a - 2b) + 4x)

So, the simplified expression is (a - 2b - 4x)(a - 2b + 4x).

The expression you provided is a quadratic expression in terms of multiple variables: a, b, and x. To simplify it, you can use the factoring method called the "difference of squares".

The expression a^2 - 4ab + 4b^2 - 16x^2 can be written as:

(a^2 - 4ab + 4b^2) - 16x^2

Now, let's focus on the first part, a^2 - 4ab + 4b^2. This part is a perfect square trinomial because it can be factored into (a - 2b)^2.

So, the expression becomes:

(a - 2b)^2 - 16x^2

Now, we can use the difference of squares identity, which states that a^2 - b^2 can be factored as (a + b)(a - b). In this case, we can rewrite the expression as:

[(a - 2b) + 4x][(a - 2b) - 4x]

And there you have it, the simplified form of the expression a^2 - 4ab + 4b^2 - 16x^2 is [(a - 2b) + 4x][(a - 2b) - 4x].