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Difficulty: HardEvaluating Algebraic Expressions

Evaluate the algebraic expression:

−3a2+4b−∣a−c∣-3a^2 + 4b - |a - c|

Given the values a=−2a = -2, b=−3b = -3, and c=5c = 5, which of the following is the correct result?

  1. -31Answer
  2. B
    -27
  3. C
    -17
  4. D
    17

Answer

The correct result is -31.
The expression requires precise substitution and adherence to the order of operations. Squaring the negative value a=−2a = -2 gives 44, which multiplied by −3-3 results in −12-12. The term 4b4b becomes 4(−3)=−124(-3) = -12. The absolute value of a−ca - c evaluates to ∣−2−5∣=∣−7∣=7|-2 - 5| = |-7| = 7. Subtracting this 77 from the sum of the first two terms yields −12−12−7=−31-12 - 12 - 7 = -31.

Step-by-Step Solution

1
Substitute the given values for aa, bb, and cc into the expression.
−3(−2)2+4(−3)−∣−2−5∣-3(-2)^2 + 4(-3) - |-2 - 5|
Correct substitution requires maintaining negative signs within parentheses to prevent sign errors.
2
Evaluate the exponent and the grouping symbol (absolute value).
The exponent term evaluates to (−2)2=4(-2)^2 = 4. The absolute value expression evaluates to ∣−7∣=7|-7| = 7.
According to the order of operations, exponents and operations inside grouping symbols must be resolved before multiplication.
3
Perform the multiplication.
−3(4)=−12-3(4) = -12 and 4(−3)=−124(-3) = -12. The expression simplifies to −12−12−7-12 - 12 - 7.
Multiplication must be executed before addition and subtraction.
4
Perform the final subtraction operations from left to right.
−12−12−7=−24−7=−31-12 - 12 - 7 = -24 - 7 = -31.
Combining the remaining terms provides the final evaluated result.

Key Concept

Evaluating algebraic expressions involving negative integers, exponents, and absolute values
Estimated Time:1m 0s
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Topics

Evaluating Algebraic Expressions

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