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Difficulty: MediumEvaluating Algebraic Expressions

Complete the evaluation of the algebraic expression by filling in the blanks with the correct numerical values.

Answer:Evaluate the algebraic expression 5x2y−3z3x5x^2y - \frac{3z^3}{x} for the given variables x=−2x = -2, y=3y = 3, and z=−2z = -2.

Step 1: The numerical value of the first term, 5x2y5x^2y, is 【60】.
Step 2: The numerical value of the second term (including the negative sign), −3z3x-\frac{3z^3}{x}, is 【-12】.
Step 3: The final evaluated value of the entire expression is 【48】.

Answer

The first term evaluates to 60, the second term evaluates to -12, and the final combined expression value is 48.
The expression requires careful substitution and order of operations. First, squaring x=−2x = -2 yields 44, making the first term 5(4)(3)=605(4)(3) = 60. Next, cubing z=−2z = -2 gives −8-8, resulting in a numerator of −24-24. Dividing by x=−2x = -2 gives 1212. Applying the subtraction sign makes the second term −12-12. Adding these components yields 60−12=4860 - 12 = 48.

Step-by-Step Solution

1
Substitute the given values into the first term 5x2y5x^2y.
5(−2)2(3)5(-2)^2(3)
Variables must be replaced with their assigned numerical values.
2
Evaluate the exponent and multiply to find the value of the first term.
5(4)(3)=605(4)(3) = 60
According to the order of operations, exponents are evaluated before multiplication.
3
Substitute the given values into the second term −3z3x-\frac{3z^3}{x}.
−3(−2)3−2-\frac{3(-2)^3}{-2}
Preparing the rational term for evaluation.
4
Evaluate the exponent in the numerator.
−3(−8)−2-\frac{3(-8)}{-2}
The cube of a negative number remains negative, so (−2)3=−8(-2)^3 = -8.
5
Multiply the numerator and simplify the fraction.
−−24−2=−(12)=−12-\frac{-24}{-2} = - (12) = -12
Multiplying 3 by -8 gives -24. Dividing -24 by -2 gives positive 12. Applying the negative sign in front results in -12.
6
Combine the evaluated terms to find the final result.
60−12=4860 - 12 = 48
Summing the intermediate values yields the final expression value.

Key Concept

Evaluating algebraic expressions involves correctly applying variable substitution, managing negative signs, and strictly following the order of operations.
Estimated Time:1m 0s
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Topics

Evaluating Algebraic Expressions

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