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Zorluk: OrtaEvaluating Algebraic Expressions

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

Cevap: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】.

Cevap

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.

Adım Adım Çözüm

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.

Anahtar Kavram

Evaluating algebraic expressions involves correctly applying variable substitution, managing negative signs, and strictly following the order of operations.
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Evaluating Algebraic Expressions

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