Simplify: 13 B 6 − 44 B 6 13b^6 - 44b^6 13 B 6 − 44 B 6 Enter The Original Expression If It Cannot Be Simplified.Enter The Correct Answer.

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Introduction

When dealing with algebraic expressions, simplification is a crucial step to make the expression more manageable and easier to work with. In this case, we are given the expression 13b6−44b613b^6 - 44b^6 and we need to simplify it. The goal is to combine like terms and reduce the expression to its simplest form.

Understanding the Expression

Before we start simplifying, let's take a closer look at the expression. We have two terms: 13b613b^6 and −44b6-44b^6. Both terms have the same variable, bb, raised to the power of 6. This means that they are like terms, and we can combine them by adding or subtracting their coefficients.

Combining Like Terms

To simplify the expression, we need to combine the like terms. We can do this by adding or subtracting the coefficients of the terms. In this case, we have:

13b6−44b613b^6 - 44b^6

We can combine the two terms by subtracting their coefficients:

13b6−44b6=(13−44)b613b^6 - 44b^6 = (13 - 44)b^6

Simplifying the Expression

Now that we have combined the like terms, we can simplify the expression further. We can simplify the coefficient by subtracting 44 from 13:

13−44=−3113 - 44 = -31

So, the simplified expression is:

−31b6-31b^6

Conclusion

In conclusion, the simplified expression is −31b6-31b^6. This is the simplest form of the original expression, and it is easier to work with than the original expression.

Final Answer

The final answer is: −31b6\boxed{-31b^6}

Discussion

This problem is a great example of how to simplify algebraic expressions by combining like terms. By following the steps outlined above, we can simplify the expression and arrive at the final answer. This type of problem is commonly seen in algebra and is an important skill to have when working with algebraic expressions.

Tips and Tricks

Here are some tips and tricks to help you simplify algebraic expressions:

  • Always look for like terms and combine them by adding or subtracting their coefficients.
  • Use the distributive property to expand expressions and make it easier to combine like terms.
  • Simplify coefficients by adding or subtracting them.
  • Use parentheses to group terms and make it easier to combine like terms.

Common Mistakes

Here are some common mistakes to avoid when simplifying algebraic expressions:

  • Failing to combine like terms.
  • Not simplifying coefficients.
  • Not using parentheses to group terms.
  • Not following the order of operations.

Real-World Applications

Simplifying algebraic expressions has many real-world applications. For example, in physics, we use algebraic expressions to describe the motion of objects. By simplifying these expressions, we can make it easier to solve problems and arrive at the correct answer.

Conclusion

In conclusion, simplifying algebraic expressions is an important skill to have when working with algebra. By following the steps outlined above and avoiding common mistakes, we can simplify expressions and arrive at the final answer. This type of problem is commonly seen in algebra and is an important skill to have when working with algebraic expressions.

Final Thoughts

Simplifying algebraic expressions is not just about combining like terms and simplifying coefficients. It's about understanding the underlying structure of the expression and using that understanding to simplify it. By developing this skill, we can make it easier to work with algebraic expressions and arrive at the correct answer.

Introduction

In our previous article, we simplified the expression 13b6−44b613b^6 - 44b^6 to −31b6-31b^6. However, we know that there are many more questions and doubts that readers may have. In this article, we will address some of the most frequently asked questions and provide additional information to help readers understand the concept of simplifying algebraic expressions.

Q&A

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 identify like terms in an expression?

A: To identify like terms, look for terms that have the same variable raised to the same power. For example, in the expression 2x2+3x2+4x2x^2 + 3x^2 + 4x, the terms 2x22x^2 and 3x23x^2 are like terms because they have the same variable xx raised to the same power 22.

Q: Can I combine like terms that have different coefficients?

A: Yes, you can combine like terms that have different coefficients. For example, in the expression 2x+3x2x + 3x, you can combine the two terms to get 5x5x.

Q: What is the distributive property, and how do I use it to simplify expressions?

A: The distributive property is a rule that allows you to multiply a single term by multiple terms. To use the distributive property, multiply each term inside the parentheses by the term outside the parentheses. For example, in the expression 2(x+3)2(x + 3), you can use the distributive property to get 2x+62x + 6.

Q: Can I simplify expressions with variables in the denominator?

A: Yes, you can simplify expressions with variables in the denominator. However, you need to follow the rules of exponents and simplify the expression carefully. For example, in the expression 2xx2\frac{2x}{x^2}, you can simplify the expression to 2x\frac{2}{x}.

Q: What is the order of operations, and how do I use it to simplify expressions?

A: The order of operations is a set of rules that tells you which operations to perform first when simplifying expressions. The order of operations is:

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

Q: Can I simplify expressions with negative coefficients?

A: Yes, you can simplify expressions with negative coefficients. However, you need to follow the rules of exponents and simplify the expression carefully. For example, in the expression −2x2-2x^2, you can simplify the expression to −2x2-2x^2.

Conclusion

In conclusion, simplifying algebraic expressions is an important skill to have when working with algebra. By following the steps outlined above and using the distributive property, you can simplify expressions and arrive at the final answer. Remember to identify like terms, combine them, and simplify coefficients to get the final answer.

Final Thoughts

Simplifying algebraic expressions is not just about combining like terms and simplifying coefficients. It's about understanding the underlying structure of the expression and using that understanding to simplify it. By developing this skill, you can make it easier to work with algebraic expressions and arrive at the correct answer.

Additional Resources

If you want to learn more about simplifying algebraic expressions, here are some additional resources that you can use:

  • Khan Academy: Simplifying Algebraic Expressions
  • Mathway: Simplifying Algebraic Expressions
  • Wolfram Alpha: Simplifying Algebraic Expressions

Final Answer

The final answer is: −31b6\boxed{-31b^6}