The problem asks us to expand the product of two binomials: $(2x+7)(2x-7)$.

1. Problem Description

The problem asks us to expand the product of two binomials: $(2x+7)(2x-7)$.

2. Solution Steps

We can expand the product using the distributive property (also known as the FOIL method):

$(2x+7)(2x-7) = (2x)(2x) + (2x)(-7) + (7)(2x) + (7)(-7)$

$= 4x^2 - 14x + 14x - 49$

Since $-14x + 14x = 0$, we have

$4x^2 - 49$

Alternatively, we can recognize that this is in the form of a difference of squares: $(a+b)(a-b) = a^2 - b^2$. In this case, $a = 2x$ and $b = 7$. Therefore:

$(2x+7)(2x-7) = (2x)^2 - (7)^2$

$= 4x^2 - 49$

3. Final Answer

$4x^2 - 49$