College Math Placement Practice Test

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What is the value of the expression 7^2 - 4^2?

The correct answer is: 33

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.