In a specific algorithm, the output value is determined by the algebraic rule 2m^2n - 3n^2… — Armed Services Vocational Aptitude Battery (ASVAB)

In a specific algorithm, the output value is determined by the algebraic rule $2m^2n - 3n^2$ . Which of the following is the resulting output when the algorithm processes the inputs $m = -4$ and $n = -3$ ?

-123Answer
B
-69
C
69
D
-219

Answer

The correct evaluated result is -123.

The correct answer is found by substituting the numerical values for the variables and strictly adhering to the order of operations. First, squaring the negative integers results in positive values, transforming the expression to 2(16)(-3) - 3(9). Multiplying the terms gives -96 and 27, respectively. Finally, subtracting 27 from -96 produces a final value of -123.

Step-by-Step Solution

Substitute the given values

m = -4

and

n = -3

into the expression

2m^2n - 3n^2

2(-4)^2(-3) - 3(-3)^2

Direct substitution of variables with their numerical values is the required first step to evaluate any algebraic expression.

Evaluate the exponents according to the order of operations (PEMDAS).

(-4)^2 = 16

and

(-3)^2 = 9

. The expression becomes

2(16)(-3) - 3(9)

Exponents must be calculated before multiplication to maintain mathematical accuracy. A negative number raised to an even power results in a positive number.

Perform the multiplication operations from left to right.

For the first term:

2(16) = 32

, and

32(-3) = -96

. For the second term:

3(9) = 27

. The expression is now

-96 - 27

Multiplication precedes subtraction in the order of operations.

Perform the final subtraction to find the total value.

-96 - 27 = -123

Combining the remaining terms yields the final evaluated numerical result of the polynomial.

Key Concept

Evaluating algebraic expressions with negative integers using substitution and the order of operations.

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