College Math Placement Practice Test

To find the value of the expression \( 7^2 - 4^2 \), we will calculate the squares of the numbers first.

Calculating \( 7^2 \):

\[

7^2 = 49

\]

Calculating \( 4^2 \):

\[

4^2 = 16

\]

Now, we subtract these two results:

\[

49 - 16 = 33

\]

Thus, the value of the expression \( 7^2 - 4^2 \) is 33. This demonstrates a straightforward application of the formula for the difference of squares, where \( a^2 - b^2 = (a-b)(a+b) \). Here, \( a = 7 \) and \( b = 4 \). Applying this formula:

\[

7^2 - 4^2 = (7-4)(7+4) = 3 \times 11 = 33

\]

This confirms that the calculation is accurate, leading to the conclusion that the correct value of the expression is indeed 33.