Evaluate $(-6)^2-7^2$
A) -85
B) -13
C) 169
D) 85
Answer (2)
Calculate ( − 6 ) 2 = 36 .
Calculate 7 2 = 49 .
Subtract the results: 36 − 49 = − 13 .
The final answer is − 13 .
Explanation
Understanding the Problem We are asked to evaluate the expression ( − 6 ) 2 − 7 2 . This involves finding the square of -6 and the square of 7, and then subtracting the latter from the former.
Calculating (-6)^2 First, let's calculate ( − 6 ) 2 . Remember that squaring a negative number results in a positive number. So, ( − 6 ) 2 = ( − 6 ) × ( − 6 ) = 36 .
Calculating 7^2 Next, let's calculate 7 2 . This is simply 7 × 7 = 49 .
Subtracting the Results Now, we subtract 7 2 from ( − 6 ) 2 , which means we calculate 36 − 49 . This gives us 36 − 49 = − 13 .
Final Answer Therefore, ( − 6 ) 2 − 7 2 = − 13 . Comparing this to the given options, we see that the correct answer is B) -13.
Examples
Understanding how to evaluate expressions with squares and subtraction is useful in many areas, such as physics (calculating kinetic energy), engineering (stress analysis), and computer graphics (transformations). For example, if you're calculating the change in area of a square when the side length changes, you'll use similar calculations involving squares and subtraction. Suppose you have a square with side length 7, and you reduce the side length to 6. The change in area is 7 2 − 6 2 = 49 − 36 = 13 .
The evaluation of ( − 6 ) 2 − 7 2 results in − 13 . Thus, the correct answer is B) -13.
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