Question

Find the area of the rectangle.
( 5x - 4 )
( 5x + 4 )

Answer 1

To find the area of the rectangle defined by the expressions \( (5x - 4) \) and \( (5x + 4) \), we can multiply these two expressions together:

\[
\text{Area} = (5x - 4)(5x + 4)
\]

This expression represents the product of a difference of squares. We can use the formula:

\[
a^2 - b^2 = (a-b)(a+b)
\]

In our case, let \( a = 5x \) and \( b = 4 \). Thus, we have:

\[
\text{Area} = (5x)^2 - (4)^2
\]

Calculating each term gives:

\[
(5x)^2 = 25x^2
\]
\[
(4)^2 = 16
\]

Now substituting back, we have:

\[
\text{Area} = 25x^2 - 16
\]

Thus, the area of the rectangle is:

\[
\boxed{25x^2 - 16}
\]