To solve the expression [tex]\((2x + 5)(2x - 5)\)[/tex], we will use the difference of squares formula. The difference of squares formula states that for any numbers [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
[tex]\[
(a + b)(a - b) = a^2 - b^2
\][/tex]
Here, [tex]\(a = 2x\)[/tex] and [tex]\(b = 5\)[/tex].
1. Square the first term [tex]\(2x\)[/tex]:
[tex]\[
(2x)^2 = 4x^2
\][/tex]
2. Square the second term [tex]\(5\)[/tex]:
[tex]\[
5^2 = 25
\][/tex]
3. Apply the formula:
[tex]\[
(2x + 5)(2x - 5) = (2x)^2 - 5^2 = 4x^2 - 25
\][/tex]
Thus, the expanded expression is:
[tex]\[
4x^2 - 25
\][/tex]
