Evaluate The Algebraic Expression For The Given Values Of The Variables.Expression: \[$-x^2 - 5xy + 5y^3\$\]Values: \[$x = -3\$\], \[$y = -2\$\]Simplified Result: \[$\square \square\$\](Simplify Your Answer.)

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Introduction

Algebraic expressions are a fundamental concept in mathematics, and evaluating them is a crucial skill for students and professionals alike. In this article, we will explore the process of evaluating an algebraic expression for given values of the variables. We will use a specific expression and values as an example to illustrate the steps involved.

The Algebraic Expression

The given algebraic expression is:

−x2−5xy+5y3-x^2 - 5xy + 5y^3

This expression consists of three terms: a quadratic term, a linear term, and a cubic term. The variables involved are xx and yy, and the coefficients are −1-1, −5-5, and 55 respectively.

The Given Values

The given values of the variables are:

x=−3x = -3

y=−2y = -2

These values will be substituted into the algebraic expression to evaluate it.

Evaluating the Expression

To evaluate the expression, we will substitute the given values of xx and yy into the expression and simplify the result.

Step 1: Substitute the Values of xx and yy

We will start by substituting the values of xx and yy into the expression:

−(−3)2−5(−3)(−2)+5(−2)3-(-3)^2 - 5(-3)(-2) + 5(-2)^3

Step 2: Simplify the Expression

Next, we will simplify the expression by evaluating the exponents and multiplying the coefficients:

−9−30−40-9 - 30 - 40

Step 3: Combine Like Terms

Finally, we will combine the like terms to get the final result:

−79-79

Conclusion

In this article, we evaluated an algebraic expression for given values of the variables. We used a specific expression and values as an example to illustrate the steps involved. By following these steps, we can evaluate any algebraic expression for given values of the variables.

Tips and Tricks

  • Make sure to substitute the values of the variables correctly into the expression.
  • Simplify the expression by evaluating the exponents and multiplying the coefficients.
  • Combine like terms to get the final result.

Common Mistakes

  • Failing to substitute the values of the variables correctly into the expression.
  • Not simplifying the expression by evaluating the exponents and multiplying the coefficients.
  • Not combining like terms to get the final result.

Real-World Applications

Evaluating algebraic expressions is a crucial skill in many real-world applications, including:

  • Science and engineering: Algebraic expressions are used to model real-world phenomena, such as the motion of objects and the behavior of electrical circuits.
  • Economics: Algebraic expressions are used to model economic systems and make predictions about future trends.
  • Computer science: Algebraic expressions are used to write algorithms and solve problems in computer science.

Final Result

The final result of evaluating the algebraic expression for the given values of the variables is:

−79-79

This result can be used to make predictions and solve problems in various fields.

Frequently Asked Questions

  • What is an algebraic expression? An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations.
  • How do I evaluate an algebraic expression? To evaluate an algebraic expression, you need to substitute the values of the variables into the expression and simplify the result.
  • What are the common mistakes when evaluating algebraic expressions? The common mistakes when evaluating algebraic expressions include failing to substitute the values of the variables correctly into the expression, not simplifying the expression by evaluating the exponents and multiplying the coefficients, and not combining like terms to get the final result.

Conclusion

Evaluating algebraic expressions is a crucial skill in mathematics and has many real-world applications. By following the steps outlined in this article, you can evaluate any algebraic expression for given values of the variables. Remember to substitute the values of the variables correctly into the expression, simplify the expression by evaluating the exponents and multiplying the coefficients, and combine like terms to get the final result.

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Introduction

Evaluating algebraic expressions is a crucial skill in mathematics, and it's essential to understand the concepts and techniques involved. In this article, we will provide a Q&A guide to help you evaluate algebraic expressions with confidence.

Q&A

Q1: What is an algebraic expression?

A1: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations.

Q2: How do I evaluate an algebraic expression?

A2: To evaluate an algebraic expression, you need to substitute the values of the variables into the expression and simplify the result.

Q3: What are the steps involved in evaluating an algebraic expression?

A3: The steps involved in evaluating an algebraic expression are:

  1. Substitute the values of the variables into the expression.
  2. Simplify the expression by evaluating the exponents and multiplying the coefficients.
  3. Combine like terms to get the final result.

Q4: What are the common mistakes when evaluating algebraic expressions?

A4: The common mistakes when evaluating algebraic expressions include:

  • Failing to substitute the values of the variables correctly into the expression.
  • Not simplifying the expression by evaluating the exponents and multiplying the coefficients.
  • Not combining like terms to get the final result.

Q5: How do I handle negative exponents?

A5: When handling negative exponents, you need to rewrite the expression with a positive exponent by taking the reciprocal of the base.

Q6: How do I handle fractional exponents?

A6: When handling fractional exponents, you need to rewrite the expression with a positive exponent by taking the root of the base.

Q7: How do I handle exponents with variables?

A7: When handling exponents with variables, you need to follow the order of operations (PEMDAS) and evaluate the expression inside the parentheses first.

Q8: How do I handle expressions with multiple variables?

A8: When handling expressions with multiple variables, you need to substitute the values of the variables into the expression and simplify the result.

Q9: How do I handle expressions with absolute values?

A9: When handling expressions with absolute values, you need to evaluate the expression inside the absolute value first and then take the absolute value of the result.

Q10: How do I handle expressions with fractions?

A10: When handling expressions with fractions, you need to simplify the fraction by dividing the numerator and denominator by their greatest common divisor.

Tips and Tricks

  • Make sure to substitute the values of the variables correctly into the expression.
  • Simplify the expression by evaluating the exponents and multiplying the coefficients.
  • Combine like terms to get the final result.
  • Handle negative exponents by rewriting the expression with a positive exponent.
  • Handle fractional exponents by rewriting the expression with a positive exponent.
  • Handle exponents with variables by following the order of operations (PEMDAS).
  • Handle expressions with multiple variables by substituting the values of the variables into the expression and simplifying the result.
  • Handle expressions with absolute values by evaluating the expression inside the absolute value first and then taking the absolute value of the result.
  • Handle expressions with fractions by simplifying the fraction by dividing the numerator and denominator by their greatest common divisor.

Common Mistakes

  • Failing to substitute the values of the variables correctly into the expression.
  • Not simplifying the expression by evaluating the exponents and multiplying the coefficients.
  • Not combining like terms to get the final result.
  • Not handling negative exponents correctly.
  • Not handling fractional exponents correctly.
  • Not handling exponents with variables correctly.
  • Not handling expressions with multiple variables correctly.
  • Not handling expressions with absolute values correctly.
  • Not handling expressions with fractions correctly.

Real-World Applications

Evaluating algebraic expressions is a crucial skill in many real-world applications, including:

  • Science and engineering: Algebraic expressions are used to model real-world phenomena, such as the motion of objects and the behavior of electrical circuits.
  • Economics: Algebraic expressions are used to model economic systems and make predictions about future trends.
  • Computer science: Algebraic expressions are used to write algorithms and solve problems in computer science.

Final Result

By following the steps outlined in this article, you can evaluate any algebraic expression with confidence. Remember to substitute the values of the variables correctly into the expression, simplify the expression by evaluating the exponents and multiplying the coefficients, and combine like terms to get the final result.

Frequently Asked Questions

  • What is an algebraic expression? An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations.
  • How do I evaluate an algebraic expression? To evaluate an algebraic expression, you need to substitute the values of the variables into the expression and simplify the result.
  • What are the common mistakes when evaluating algebraic expressions? The common mistakes when evaluating algebraic expressions include failing to substitute the values of the variables correctly into the expression, not simplifying the expression by evaluating the exponents and multiplying the coefficients, and not combining like terms to get the final result.

Conclusion

Evaluating algebraic expressions is a crucial skill in mathematics, and it's essential to understand the concepts and techniques involved. By following the steps outlined in this article, you can evaluate any algebraic expression with confidence. Remember to substitute the values of the variables correctly into the expression, simplify the expression by evaluating the exponents and multiplying the coefficients, and combine like terms to get the final result.