Certainly, let's find the product step by step.
We are given the expression [tex]\((x + 2y)(x - 2y)\)[/tex].
Step 1: Identify the type of expression.
The given expression is a difference of squares. A difference of squares follows the formula:
[tex]\[
(a + b)(a - b) = a^2 - b^2
\][/tex]
Step 2: Apply the difference of squares formula.
In this scenario, we can identify [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
[tex]\[
a = x \quad \text{and} \quad b = 2y
\][/tex]
Step 3: Substitute [tex]\(a\)[/tex] and [tex]\(b\)[/tex] into the formula.
Using the difference of squares formula, we get:
[tex]\[
(x + 2y)(x - 2y) = x^2 - (2y)^2
\][/tex]
Step 4: Simplify the squared term [tex]\((2y)^2\)[/tex].
[tex]\[
(2y)^2 = 4y^2
\][/tex]
Step 5: Substitute back to get the final result.
[tex]\[
x^2 - 4y^2
\][/tex]
Therefore, the product [tex]\((x + 2y)(x - 2y)\)[/tex] simplifies to:
[tex]\[
\boxed{x^2 - 4y^2}
\][/tex]
