What Is The Difference Of The Two Polynomials?$(7y^2 + 6xy) - (-2xy + 3$\]A. $7y^2 + 8xy - 3$ B. $7y^2 + 8xy + 3$ C. $7y^2 + 4xy - 3$ D. $7y^2 + 4xy + 3$
Understanding Polynomials and Their Operations
Polynomials are algebraic expressions consisting of variables and coefficients combined using addition, subtraction, and multiplication. They are a fundamental concept in mathematics, and understanding their operations is crucial for solving various mathematical problems. In this article, we will explore the difference of two polynomials and how to calculate it.
What is a Polynomial?
A polynomial is an expression consisting of variables and coefficients combined using addition, subtraction, and multiplication. It can be written in the form:
a_n x^n + a_(n-1) x^(n-1) + ... + a_1 x + a_0
where a_n, a_(n-1), ..., a_1, a_0 are coefficients, and x is the variable.
Types of Polynomials
Polynomials can be classified into different types based on their degree. The degree of a polynomial is the highest power of the variable in the polynomial.
- Monomial: A polynomial with only one term is called a monomial. For example, 3x^2 is a monomial.
- Binomial: A polynomial with two terms is called a binomial. For example, 3x^2 + 2x is a binomial.
- Trinomial: A polynomial with three terms is called a trinomial. For example, 3x^2 + 2x + 1 is a trinomial.
- Polynomial of degree n: A polynomial with n terms is called a polynomial of degree n.
Operations on Polynomials
Polynomials can be added, subtracted, and multiplied using the following rules:
- Addition: When adding two polynomials, we add the corresponding terms.
- Subtraction: When subtracting two polynomials, we subtract the corresponding terms.
- Multiplication: When multiplying two polynomials, we multiply each term of the first polynomial by each term of the second polynomial.
Calculating the Difference of Two Polynomials
Now, let's calculate the difference of two polynomials using the given example:
(7y^2 + 6xy) - (-2xy + 3)
To calculate the difference, we need to subtract the corresponding terms.
(7y^2 + 6xy) - (-2xy + 3)
= 7y^2 + 6xy + 2xy - 3
= 7y^2 + 8xy - 3
Therefore, the difference of the two polynomials is 7y^2 + 8xy - 3.
Conclusion
In conclusion, understanding the difference of two polynomials is crucial for solving various mathematical problems. By following the rules of addition, subtraction, and multiplication, we can calculate the difference of two polynomials. In this article, we explored the concept of polynomials, their operations, and how to calculate the difference of two polynomials using a given example.
Answer
The correct answer is A. 7y^2 + 8xy - 3.
References
Frequently Asked Questions
In this article, we will answer some frequently asked questions about the difference of two polynomials.
Q: What is the difference of two polynomials?
A: The difference of two polynomials is the result of subtracting one polynomial from another. It is calculated by subtracting the corresponding terms of the two polynomials.
Q: How do I calculate the difference of two polynomials?
A: To calculate the difference of two polynomials, you need to subtract the corresponding terms of the two polynomials. For example, if we have two polynomials:
(7y^2 + 6xy) - (-2xy + 3)
We need to subtract the corresponding terms:
= 7y^2 + 6xy + 2xy - 3
= 7y^2 + 8xy - 3
Q: What is the order of operations when calculating the difference of two polynomials?
A: When calculating the difference of two polynomials, you need to follow the order of operations:
- Subtract the corresponding terms.
- Combine like terms.
Q: Can I add polynomials and then subtract them?
A: Yes, you can add polynomials and then subtract them. However, it is not necessary to do so. You can simply subtract the polynomials directly.
Q: What is the difference between adding and subtracting polynomials?
A: Adding polynomials involves combining like terms, while subtracting polynomials involves subtracting the corresponding terms.
Q: Can I multiply polynomials and then subtract them?
A: No, you cannot multiply polynomials and then subtract them. Multiplying polynomials involves multiplying each term of one polynomial by each term of the other polynomial, while subtracting polynomials involves subtracting the corresponding terms.
Q: What is the difference between a polynomial and an expression?
A: A polynomial is an expression consisting of variables and coefficients combined using addition, subtraction, and multiplication. An expression is a general term that can include variables, coefficients, and mathematical operations.
Q: Can I simplify a polynomial by combining like terms?
A: Yes, you can simplify a polynomial by combining like terms. This involves adding or subtracting the coefficients of like terms.
Q: What is the importance of understanding the difference of two polynomials?
A: Understanding the difference of two polynomials is crucial for solving various mathematical problems, including algebraic equations and inequalities. It is also essential for understanding more advanced mathematical concepts, such as calculus and differential equations.
Conclusion
In conclusion, understanding the difference of two polynomials is a fundamental concept in mathematics. By following the rules of addition, subtraction, and multiplication, we can calculate the difference of two polynomials. In this article, we answered some frequently asked questions about the difference of two polynomials and provided examples to illustrate the concept.