To find the product of the expression [tex]\((x + 2y)(x - 2y)\)[/tex], we can use the formula for the difference of squares. This formula states that for any two terms [tex]\(a\)[/tex] and [tex]\(b\)[/tex],
[tex]\[
(a + b)(a - b) = a^2 - b^2.
\][/tex]
In this case, we can identify [tex]\(a = x\)[/tex] and [tex]\(b = 2y\)[/tex].
Now, applying the difference of squares formula to the given expression [tex]\((x + 2y)(x - 2y)\)[/tex]:
[tex]\[
(x + 2y)(x - 2y) = x^2 - (2y)^2.
\][/tex]
Next, we need to simplify [tex]\((2y)^2\)[/tex]. When squaring [tex]\(2y\)[/tex], we get:
[tex]\[
(2y)^2 = 2^2 \cdot y^2 = 4y^2.
\][/tex]
So the expression becomes:
[tex]\[
x^2 - 4y^2.
\][/tex]
Therefore, the product of [tex]\((x + 2y)(x - 2y)\)[/tex] is:
[tex]\[
x^2 - 4y^2.
\][/tex]
