Find The Difference: ( 3 X 2 − 2 X ) − ( − 4 X 4 + 3 X 2 − 3 X ) \begin{array}{c} (3x^2 - 2x) - (-4x^4 + 3x^2 - 3x) \\ \end{array} ( 3 X 2 − 2 X ) − ( − 4 X 4 + 3 X 2 − 3 X ) ​ Calculate And Provide The Result In The Form [?]x^4 + [?]x^2 + [?]x$.

by ADMIN 247 views

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill to master. In this article, we will focus on finding the difference between two given algebraic expressions and providing the result in the required form. We will use a step-by-step approach to simplify the expression and arrive at the final answer.

The Given Expression

The given expression is:

(3x2−2x)−(−4x4+3x2−3x){(3x^2 - 2x) - (-4x^4 + 3x^2 - 3x)}

Our goal is to simplify this expression and provide the result in the form:

?x4+?x2+?x{?x^4 + ?x^2 + ?x}

Step 1: Distribute the Negative Sign

To simplify the given expression, we need to distribute the negative sign to the terms inside the second set of parentheses. This will change the signs of all the terms inside the parentheses.

(3x2−2x)−(−4x4+3x2−3x)=3x2−2x+4x4−3x2+3x{(3x^2 - 2x) - (-4x^4 + 3x^2 - 3x) = 3x^2 - 2x + 4x^4 - 3x^2 + 3x}

Step 2: Combine Like Terms

Now that we have distributed the negative sign, we can combine like terms. Like terms are terms that have the same variable and exponent. In this case, we have two terms with the variable x^2, and two terms with the variable x.

3x2−2x+4x4−3x2+3x=4x4+(3x2−3x2)+(−2x+3x){3x^2 - 2x + 4x^4 - 3x^2 + 3x = 4x^4 + (3x^2 - 3x^2) + (-2x + 3x)}

Step 3: Simplify the Expression

Now that we have combined like terms, we can simplify the expression further. The term (3x^2 - 3x^2) is equal to zero, and the term (-2x + 3x) is equal to x.

4x4+(3x2−3x2)+(−2x+3x)=4x4+0+x=4x4+x{4x^4 + (3x^2 - 3x^2) + (-2x + 3x) = 4x^4 + 0 + x = 4x^4 + x}

The Final Answer

Therefore, the simplified expression is:

4x4+x{4x^4 + x}

This is the final answer in the required form.

Conclusion

In this article, we have simplified the given algebraic expression using a step-by-step approach. We distributed the negative sign, combined like terms, and simplified the expression to arrive at the final answer. This process requires a good understanding of algebraic expressions and the rules of simplification. With practice and patience, anyone can master this skill and become proficient in simplifying algebraic expressions.

Key Takeaways

  • Distributing the negative sign changes the signs of all the terms inside the parentheses.
  • Combining like terms involves adding or subtracting terms with the same variable and exponent.
  • Simplifying an expression involves removing any unnecessary terms or operations.

Practice Problems

To practice simplifying algebraic expressions, try the following problems:

  1. Simplify the expression: (2x^2 + 3x) - (x^2 - 2x)
  2. Simplify the expression: (4x^3 - 2x^2) + (3x^3 + 2x^2)
  3. Simplify the expression: (x^2 + 2x) - (x^2 - 3x)

References

Glossary

  • Algebraic Expression: A mathematical expression that consists of variables, constants, and mathematical operations.
  • Like Terms: Terms that have the same variable and exponent.
  • Simplifying: Removing any unnecessary terms or operations from an expression.
    Frequently Asked Questions: Simplifying Algebraic Expressions =============================================================

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. It is a way of representing a mathematical relationship between variables and constants.

Q: What is the difference between a like term and a unlike term?

A: Like terms are terms that have the same variable and exponent. Unlike terms are terms that have different variables or exponents.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to follow these steps:

  1. Distribute the negative sign to the terms inside the second set of parentheses.
  2. Combine like terms by adding or subtracting terms with the same variable and exponent.
  3. Simplify the expression by removing any unnecessary terms or operations.

Q: What is the order of operations in simplifying algebraic expressions?

A: The order of operations in simplifying algebraic expressions is:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I handle negative signs in algebraic expressions?

A: When simplifying algebraic expressions, you need to distribute the negative sign to the terms inside the second set of parentheses. This will change the signs of all the terms inside the parentheses.

Q: What is the difference between a variable and a constant?

A: A variable is a letter or symbol that represents a value that can change. A constant is a value that does not change.

Q: How do I simplify an expression with multiple variables?

A: To simplify an expression with multiple variables, you need to follow the same steps as before:

  1. Distribute the negative sign to the terms inside the second set of parentheses.
  2. Combine like terms by adding or subtracting terms with the same variable and exponent.
  3. Simplify the expression by removing any unnecessary terms or operations.

Q: What is the final answer in the form [?]x^4 + [?]x^2 + [?]x?

A: The final answer in the form [?]x^4 + [?]x^2 + [?]x is the simplified expression after combining like terms and removing any unnecessary terms or operations.

Q: How do I check my work when simplifying algebraic expressions?

A: To check your work when simplifying algebraic expressions, you need to:

  1. Plug in a value for the variable and evaluate the expression.
  2. Simplify the expression using the value you plugged in.
  3. Compare the simplified expression with the original expression.

Q: What are some common mistakes to avoid when simplifying algebraic expressions?

A: Some common mistakes to avoid when simplifying algebraic expressions include:

  • Not distributing the negative sign to the terms inside the second set of parentheses.
  • Not combining like terms.
  • Not removing unnecessary terms or operations.
  • Not checking your work.

Q: How can I practice simplifying algebraic expressions?

A: You can practice simplifying algebraic expressions by:

  • Working on practice problems.
  • Using online resources and tools.
  • Asking a teacher or tutor for help.
  • Joining a study group or online community.

Q: What are some real-world applications of simplifying algebraic expressions?

A: Simplifying algebraic expressions has many real-world applications, including:

  • Physics and engineering: Simplifying algebraic expressions is used to solve problems in physics and engineering, such as calculating the trajectory of a projectile or the stress on a beam.
  • Computer science: Simplifying algebraic expressions is used in computer science to optimize algorithms and improve the performance of computer programs.
  • Economics: Simplifying algebraic expressions is used in economics to model and analyze economic systems.

Conclusion

Simplifying algebraic expressions is a crucial skill in mathematics and has many real-world applications. By following the steps outlined in this article and practicing regularly, you can become proficient in simplifying algebraic expressions and apply this skill to a wide range of problems.