Which Expression Can Be Used To Find The Difference Of The Polynomials?A. $(4m - 5) - (6m - 7 + 2n$\] B. $(4m - 5) + (6m + 7 + 2n$\] C. $(4m - 5) + (-6m + 7 + 2n$\] D. $(4m - 5) + (-6m - 7 - 2n$\] E. $(4m - 5) +

by ADMIN 216 views

Introduction

In algebra, polynomials are expressions consisting of variables and coefficients combined using only addition, subtraction, and multiplication. When dealing with polynomials, it's often necessary to find their difference, which involves subtracting one polynomial from another. In this article, we'll explore the concept of finding the difference of polynomials and provide a step-by-step guide on how to do it.

What is a Polynomial?

A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication. The variables in a polynomial are often represented by letters such as x, y, or z, and the coefficients are numbers that are multiplied by the variables. For example, 2x + 3y - 4 is a polynomial expression.

Types of Polynomials

There are several types of polynomials, including:

  • Monomials: A monomial is a polynomial with only one term. For example, 2x is a monomial.
  • Binomials: A binomial is a polynomial with two terms. For example, 2x + 3y is a binomial.
  • Trinomials: A trinomial is a polynomial with three terms. For example, 2x + 3y - 4 is a trinomial.
  • Polynomials with multiple variables: A polynomial can have multiple variables, such as 2x + 3y + 4z.

Finding the Difference of Polynomials

To find the difference of two polynomials, we need to subtract one polynomial from another. This involves subtracting the corresponding terms of the two polynomials.

Step 1: Identify the Polynomials

The first step in finding the difference of two polynomials is to identify the polynomials. Let's say we have two polynomials:

p(x) = 4m - 5 q(x) = 6m - 7 + 2n

Step 2: Subtract the Corresponding Terms

To find the difference of the two polynomials, we need to subtract the corresponding terms. This involves subtracting the coefficients of the corresponding terms.

p(x) - q(x) = (4m - 5) - (6m - 7 + 2n)

Step 3: Simplify the Expression

To simplify the expression, we need to combine like terms. This involves combining the terms with the same variable.

p(x) - q(x) = (4m - 6m) + (7 - 5) - 2n p(x) - q(x) = -2m + 2 - 2n

Step 4: Write the Final Answer

The final answer is the simplified expression.

p(x) - q(x) = -2m + 2 - 2n

Which Expression Can Be Used to Find the Difference of the Polynomials?

Now that we have found the difference of the two polynomials, let's look at the options provided.

A. (4m−5)−(6m−7+2n)(4m - 5) - (6m - 7 + 2n) B. (4m−5)+(6m+7+2n)(4m - 5) + (6m + 7 + 2n) C. (4m−5)+(−6m+7+2n)(4m - 5) + (-6m + 7 + 2n) D. (4m−5)+(−6m−7−2n)(4m - 5) + (-6m - 7 - 2n) E. (4m−5)+(−6m+7+2n)(4m - 5) + (-6m + 7 + 2n)

The correct answer is:

D. (4m−5)+(−6m−7−2n)(4m - 5) + (-6m - 7 - 2n)

This is because the expression in option D is the correct expression for finding the difference of the two polynomials.

Conclusion

In conclusion, finding the difference of polynomials involves subtracting one polynomial from another. This involves subtracting the corresponding terms and combining like terms. The final answer is the simplified expression. We have also looked at the options provided and determined that the correct answer is option D.

Frequently Asked Questions

  • What is a polynomial? A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication.
  • What is the difference of polynomials? The difference of polynomials is the result of subtracting one polynomial from another.
  • How do I find the difference of polynomials? To find the difference of polynomials, you need to subtract the corresponding terms and combine like terms.
  • What is the correct expression for finding the difference of the polynomials? The correct expression for finding the difference of the polynomials is (4m−5)+(−6m−7−2n)(4m - 5) + (-6m - 7 - 2n).

References

  • Algebra: A Comprehensive Introduction This book provides a comprehensive introduction to algebra, including polynomials and their differences.
  • Mathematics: A Guide for Students This book provides a guide for students on how to solve mathematical problems, including finding the difference of polynomials.

Further Reading

  • Polynomials: A Guide for Students This article provides a guide for students on how to work with polynomials, including finding their differences.
  • Algebra: A Guide for Teachers This article provides a guide for teachers on how to teach algebra, including polynomials and their differences.

Introduction

Finding the difference of polynomials is a fundamental concept in algebra that can be a bit tricky to understand. In this article, we'll answer some of the most frequently asked questions about finding the difference of polynomials.

Q: What is a polynomial?

A: A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication.

Q: What is the difference of polynomials?

A: The difference of polynomials is the result of subtracting one polynomial from another.

Q: How do I find the difference of polynomials?

A: To find the difference of polynomials, you need to subtract the corresponding terms and combine like terms.

Q: What is the correct expression for finding the difference of the polynomials?

A: The correct expression for finding the difference of the polynomials is (4m−5)+(−6m−7−2n)(4m - 5) + (-6m - 7 - 2n).

Q: Can I use a calculator to find the difference of polynomials?

A: Yes, you can use a calculator to find the difference of polynomials. However, it's always a good idea to double-check your work by hand to make sure you get the correct answer.

Q: How do I simplify the expression after finding the difference of polynomials?

A: To simplify the expression, you need to combine like terms. This involves combining the terms with the same variable.

Q: Can I use the distributive property to find the difference of polynomials?

A: Yes, you can use the distributive property to find the difference of polynomials. The distributive property states that a(b + c) = ab + ac.

Q: How do I handle negative coefficients when finding the difference of polynomials?

A: When handling negative coefficients, you need to remember that a negative coefficient is equivalent to a positive coefficient with a negative sign.

Q: Can I use the order of operations to find the difference of polynomials?

A: Yes, you can use the order of operations to find the difference of polynomials. The order of operations states that you need to perform operations in the following order: parentheses, exponents, multiplication and division, and addition and subtraction.

Q: How do I check my work when finding the difference of polynomials?

A: To check your work, you need to plug in some values for the variables and see if the expression holds true.

Q: Can I use technology to check my work when finding the difference of polynomials?

A: Yes, you can use technology to check your work when finding the difference of polynomials. Many calculators and computer algebra systems can help you check your work.

Conclusion

Finding the difference of polynomials can be a bit tricky, but with practice and patience, you can master it. Remember to always follow the order of operations and to simplify the expression after finding the difference of polynomials.

Frequently Asked Questions: Additional Resources

  • Algebra: A Comprehensive Introduction This book provides a comprehensive introduction to algebra, including polynomials and their differences.
  • Mathematics: A Guide for Students This book provides a guide for students on how to solve mathematical problems, including finding the difference of polynomials.
  • Polynomials: A Guide for Students This article provides a guide for students on how to work with polynomials, including finding their differences.
  • Algebra: A Guide for Teachers This article provides a guide for teachers on how to teach algebra, including polynomials and their differences.

References

  • Algebra: A Comprehensive Introduction This book provides a comprehensive introduction to algebra, including polynomials and their differences.
  • Mathematics: A Guide for Students This book provides a guide for students on how to solve mathematical problems, including finding the difference of polynomials.

Further Reading

  • Polynomials: A Guide for Students This article provides a guide for students on how to work with polynomials, including finding their differences.
  • Algebra: A Guide for Teachers This article provides a guide for teachers on how to teach algebra, including polynomials and their differences.