Simplify The Expression: \left(6x^2 - 3 - 5x^3\right) - \left(4x^3 + 2x^2 - 8\right ]A. 9 X 3 − 4 X 2 − 5 9x^3 - 4x^2 - 5 9 X 3 − 4 X 2 − 5 B. − 9 X 3 + 4 X 2 + 5 -9x^3 + 4x^2 + 5 − 9 X 3 + 4 X 2 + 5 C. X 3 − X 2 − 13 X 3 X^3 - X^2 - 13x^3 X 3 − X 2 − 13 X 3 D. − X 3 + X 2 + 13 X 3 -x^3 + X^2 + 13x^3 − X 3 + X 2 + 13 X 3

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Understanding the Problem

Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. In this article, we will focus on simplifying the given expression: (6x2−3−5x3)−(4x3+2x2−8)\left(6x^2 - 3 - 5x^3\right) - \left(4x^3 + 2x^2 - 8\right). We will break down the problem into manageable steps and provide a clear explanation of each step.

Step 1: Distribute the Negative Sign

The first step in simplifying the expression is to distribute the negative sign to each term inside the second set of parentheses. This means that we will change the sign of each term inside the second set of parentheses.

(6x2−3−5x3)−(4x3+2x2−8)\left(6x^2 - 3 - 5x^3\right) - \left(4x^3 + 2x^2 - 8\right)

=(6x2−3−5x3)+(−4x3−2x2+8)= \left(6x^2 - 3 - 5x^3\right) + \left(-4x^3 - 2x^2 + 8\right)

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 raised to the same power. In this case, we have two sets of like terms: 6x26x^2 and −2x2-2x^2, and −5x3-5x^3 and −4x3-4x^3.

=(6x2−3−5x3)+(−4x3−2x2+8)= \left(6x^2 - 3 - 5x^3\right) + \left(-4x^3 - 2x^2 + 8\right)

=(6x2−2x2)+(−5x3−4x3)+(−3+8)= \left(6x^2 - 2x^2\right) + \left(-5x^3 - 4x^3\right) + \left(-3 + 8\right)

Step 3: Simplify the Expression

Now that we have combined like terms, we can simplify the expression by combining the constants and the variables.

=(6x2−2x2)+(−5x3−4x3)+(−3+8)= \left(6x^2 - 2x^2\right) + \left(-5x^3 - 4x^3\right) + \left(-3 + 8\right)

=4x2−9x3+5= 4x^2 - 9x^3 + 5

Step 4: Write the Final Answer

The final answer is −9x3+4x2+5-9x^3 + 4x^2 + 5. This is the simplified form of the given expression.

Conclusion

Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. In this article, we have broken down the problem into manageable steps and provided a clear explanation of each step. We have distributed the negative sign, combined like terms, and simplified the expression to arrive at the final answer.

Frequently Asked Questions

Q: What is the difference between like terms and unlike terms?

A: Like terms are terms that have the same variable raised to the same power. Unlike terms are terms that have different variables or different powers of the same variable.

Q: How do I distribute the negative sign to each term inside the second set of parentheses?

A: To distribute the negative sign, simply change the sign of each term inside the second set of parentheses.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the like terms.

Q: What is the final answer?

A: The final answer is −9x3+4x2+5-9x^3 + 4x^2 + 5.

References

Discussion

This article has provided a step-by-step guide to simplifying the given expression. We have distributed the negative sign, combined like terms, and simplified the expression to arrive at the final answer. If you have any questions or need further clarification, please feel free to ask in the comments section below.

Related Articles

Tags

  • Algebra
  • Simplifying Expressions
  • Like Terms
  • Unlike Terms
  • Distributing the Negative Sign

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Frequently Asked Questions

Q: What is the difference between like terms and unlike terms?

A: Like terms are terms that have the same variable raised to the same power. Unlike terms are terms that have different variables or different powers of the same variable.

Q: How do I distribute the negative sign to each term inside the second set of parentheses?

A: To distribute the negative sign, simply change the sign of each term inside the second set of parentheses.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the like terms.

Q: What is the final answer?

A: The final answer is −9x3+4x2+5-9x^3 + 4x^2 + 5.

Q: Can I simplify an expression with multiple variables?

A: Yes, you can simplify an expression with multiple variables by combining like terms and distributing the negative sign.

Q: How do I know if two terms are like terms or unlike terms?

A: To determine if two terms are like terms or unlike terms, compare the variables and their powers. If the variables and their powers are the same, then the terms are like terms. If the variables and their powers are different, then the terms are unlike terms.

Q: Can I simplify an expression with a negative coefficient?

A: Yes, you can simplify an expression with a negative coefficient by distributing the negative sign and combining like terms.

Q: How do I simplify an expression with a fraction?

A: To simplify an expression with a fraction, multiply the numerator and denominator by the same value to eliminate the fraction.

Q: Can I simplify an expression with a variable in the denominator?

A: Yes, you can simplify an expression with a variable in the denominator by multiplying the numerator and denominator by the same value to eliminate the variable in the denominator.

Common Mistakes to Avoid

1. Not distributing the negative sign

When simplifying an expression, it's essential to distribute the negative sign to each term inside the second set of parentheses. Failing to do so can lead to incorrect results.

2. Not combining like terms

Combining like terms is a crucial step in simplifying an expression. Failing to do so can lead to incorrect results.

3. Not checking for unlike terms

When simplifying an expression, it's essential to check for unlike terms and combine them accordingly.

4. Not using the correct order of operations

When simplifying an expression, it's essential to follow the correct order of operations (PEMDAS). Failing to do so can lead to incorrect results.

Tips and Tricks

1. Use a systematic approach

When simplifying an expression, use a systematic approach to ensure that you don't miss any steps.

2. Check your work

When simplifying an expression, check your work to ensure that you have arrived at the correct result.

3. Use a calculator

When simplifying an expression, use a calculator to check your work and ensure that you have arrived at the correct result.

4. Practice, practice, practice

The more you practice simplifying expressions, the more comfortable you will become with the process.

Conclusion

Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. In this article, we have provided a step-by-step guide to simplifying the given expression, as well as answers to frequently asked questions and common mistakes to avoid. We have also provided tips and tricks to help you become more comfortable with simplifying expressions.

Frequently Asked Questions (FAQs)

Q: What is the difference between like terms and unlike terms?

A: Like terms are terms that have the same variable raised to the same power. Unlike terms are terms that have different variables or different powers of the same variable.

Q: How do I distribute the negative sign to each term inside the second set of parentheses?

A: To distribute the negative sign, simply change the sign of each term inside the second set of parentheses.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the like terms.

Q: What is the final answer?

A: The final answer is −9x3+4x2+5-9x^3 + 4x^2 + 5.

References

Discussion

This article has provided a step-by-step guide to simplifying the given expression, as well as answers to frequently asked questions and common mistakes to avoid. We have also provided tips and tricks to help you become more comfortable with simplifying expressions. If you have any questions or need further clarification, please feel free to ask in the comments section below.

Related Articles

Tags

  • Algebra
  • Simplifying Expressions
  • Like Terms
  • Unlike Terms
  • Distributing the Negative Sign