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Chapter 2: Problem 23

Evaluate \((3+4)^{2}\) and \(3^{2}+4^{2}\). Are they equivalent? Why or why not?

Short Answer

Expert verified
Evaluating the expressions, we find that \((3+4)^{2} = 49\) and \(3^{2}+4^{2} = 25\). As \(49 \ne 25\), the two expressions are not equivalent.

Step by step solution

01

Evaluate \((3+4)^{2}\)

First, we need to perform the operation inside the parentheses. Add 3 and 4 to get 7, then square the result. \[ (3+4)^{2} = (7)^{2} \] Now, we square 7. \[ (7)^{2} = 7 \times 7 = 49 \] Putting it all together, we have: \( (3+4)^{2} = 49 \)
02

Evaluate \(3^{2}+4^{2}\)

First, we need to square 3 and 4. \[ 3^{2} = 3 \times 3 = 9 \] \[ 4^{2} = 4 \times 4 = 16 \] Now, we need to add the two squared values. \[ 9 + 16 = 25 \] Putting it all together, we have: \( 3^{2}+4^{2} = 25 \)
03

Compare the results

Now that we have evaluated both expressions, we can compare the results. \((3+4)^2 = 49\) and \(3^2 + 4^2 = 25\). Since \(49 \ne 25\), the two expressions are not equivalent.

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