Evaluate the algebraic expression \frac{3a^2b - 4bc}{a - c} given that a = -2, b = 3, and … — Armed Services Vocational Aptitude Battery (ASVAB)

Evaluate the algebraic expression $\frac{3a^2b - 4bc}{a - c}$ given that $a = -2$ , $b = 3$ , and $c = -5$ . What is the final numerical value?

Answer: 32

Answer

The numerical value of the expression is 32.

After properly substituting the given values, evaluating the exponents, and following the order of operations, the numerator calculates to 96 and the denominator simplifies to 3. The final division of 96 by 3 yields 32.

Step-by-Step Solution

Substitute the assigned values of

a

b

, and

c

into the given algebraic expression.

\frac{3(-2)^2(3) - 4(3)(-5)}{-2 - (-5)}

Direct variable substitution is required to compute the numerical value.

Evaluate the exponent applied to the negative base.

(-2)^2 = 4

According to the order of operations (PEMDAS), exponents must be resolved prior to multiplication.

Carry out the multiplication operations in the numerator.

3(4)(3) = 36

and

4(3)(-5) = -60

Multiplication is processed from left to right within the grouping of the numerator.

Complete the subtraction operation in the numerator.

36 - (-60) = 36 + 60 = 96

Subtracting a negative quantity is algebraically identical to adding its positive counterpart.

Evaluate the subtraction operation in the denominator.

-2 - (-5) = -2 + 5 = 3

The entire denominator acts as a single grouping and must be fully simplified before division.

Divide the evaluated numerator by the evaluated denominator.

\frac{96}{3} = 32

This final arithmetic step produces the precise evaluation of the fractional expression.

Key Concept

Evaluating complex rational algebraic expressions using substitution and the order of operations with signed integers.

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