To find the product [tex]\((x + 2y)(x - 2y)\)[/tex], we can use the difference of squares formula. The difference of squares formula states that:
[tex]\[
(a + b)(a - b) = a^2 - b^2
\][/tex]
In this particular problem, we can identify [tex]\(a\)[/tex] as [tex]\(x\)[/tex] and [tex]\(b\)[/tex] as [tex]\(2y\)[/tex]. Applying the difference of squares formula, we get:
[tex]\[
(x + 2y)(x - 2y) = x^2 - (2y)^2
\][/tex]
Next, we need to simplify [tex]\((2y)^2\)[/tex]:
[tex]\[
(2y)^2 = 4y^2
\][/tex]
Substituting this back into our expression, we obtain:
[tex]\[
x^2 - 4y^2
\][/tex]
Therefore, the product of [tex]\((x + 2y)(x - 2y)\)[/tex] is:
[tex]\[
x^2 - 4y^2
\][/tex]
