If $a=2, b=-3$ and $c=4$, evaluate $a b c+b^2-a^2$
A. -24
B. -109
C. -7
D. 7
Answer (2)
Substitute the given values a = 2 , b = − 3 , and c = 4 into the expression ab c + b 2 − a 2 .
Calculate the product ab c = ( 2 ) ( − 3 ) ( 4 ) = − 24 .
Calculate b 2 = ( − 3 ) 2 = 9 and a 2 = ( 2 ) 2 = 4 .
Simplify the expression: − 24 + 9 − 4 = − 19 . The final answer is − 19 .
Explanation
Understanding the Problem We are given the values a = 2 , b = − 3 , and c = 4 . We need to evaluate the expression ab c + b 2 − a 2 .
Substituting the Values First, we substitute the given values into the expression: ab c + b 2 − a 2 = ( 2 ) ( − 3 ) ( 4 ) + ( − 3 ) 2 − ( 2 ) 2
Calculating Each Term Next, we calculate each term: ( 2 ) ( − 3 ) ( 4 ) = − 24 ( − 3 ) 2 = 9 ( 2 ) 2 = 4
Substituting Back Now, we substitute these values back into the expression: − 24 + 9 − 4 = − 19
Final Result Therefore, the value of the expression ab c + b 2 − a 2 is − 19 .
Examples
Understanding how to evaluate algebraic expressions is fundamental in many areas, such as physics and engineering. For example, in physics, you might use such expressions to calculate the potential energy of a system, where a , b , and c could represent different physical parameters like mass, velocity, and height. By substituting values into the expression, you can determine the energy stored in the system. This skill is crucial for making predictions and designing experiments.
The evaluated expression ab c + b 2 − a 2 with a = 2 , b = − 3 , and c = 4 results in − 19 . So the chosen option is not listed in the provided choices, as the closest correct result is − 19 . Therefore, it is important to check the original problem's expression for any possible typos.
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