What Is The Difference Of The Two Polynomials?$\left(7y^2 + 6xy\right) - (-2xy + 3$\]A. $7y^2 + 4xy - 3$ B. $7y^2 + 8xy - 3$ C. $7y^2 + 4xy + 3$ D. $7y^2 + 8xy + 3$
In mathematics, polynomials are algebraic expressions consisting of variables and coefficients combined using only addition, subtraction, and multiplication. When we are given two polynomials, we can find their difference by subtracting one from the other. In this article, we will explore the concept of subtracting two polynomials and provide a step-by-step solution to a given problem.
Understanding Polynomials
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, while the coefficients are numbers that are multiplied with the variables. For example, the expression 2x + 3y is a polynomial, where 2 and 3 are coefficients, and x and y are variables.
Subtracting Two Polynomials
When we are given two polynomials, we can find their difference by subtracting one from the other. To do this, we need to subtract the corresponding terms of the two polynomials. For example, if we have two polynomials:
p(x) = 2x + 3y q(x) = 4x - 2y
We can find their difference by subtracting q(x) from p(x):
p(x) - q(x) = (2x + 3y) - (4x - 2y) = 2x + 3y - 4x + 2y = -2x + 5y
Solving the Given Problem
Now, let's solve the given problem:
To find the difference of these two polynomials, we need to subtract the corresponding terms. We can start by removing the parentheses and combining like terms:
= 7y^2 + 6xy + 2xy - 3 = 7y^2 + 8xy - 3
Therefore, the difference of the two polynomials is:
Conclusion
In this article, we explored the concept of subtracting two polynomials and provided a step-by-step solution to a given problem. We learned that to find the difference of two polynomials, we need to subtract the corresponding terms and combine like terms. By following these steps, we can find the difference of any two polynomials.
Answer
The correct answer is:
A.
However, this is not the correct solution. The correct solution is:
This is the difference of the two polynomials:
Final Answer
In the previous article, we explored the concept of subtracting two polynomials and provided a step-by-step solution to a given problem. However, we received many questions from readers who wanted to know more about subtracting polynomials. In this article, we will answer some of the most frequently asked questions about subtracting polynomials.
Q: What is the difference between subtracting polynomials and adding polynomials?
A: The main difference between subtracting polynomials and adding polynomials is the operation we perform on the polynomials. When we add polynomials, we combine like terms by adding their coefficients. When we subtract polynomials, we combine like terms by subtracting their coefficients.
Q: How do I subtract a polynomial from a constant?
A: When we subtract a polynomial from a constant, we need to distribute the negative sign to all the terms in the polynomial. For example, if we have:
5 - (2x + 3y)
We can distribute the negative sign to get:
5 - 2x - 3y
Q: Can I subtract a polynomial from a polynomial with a different variable?
A: Yes, you can subtract a polynomial from a polynomial with a different variable. However, you need to make sure that the variables are not the same. For example, if we have:
2x + 3y - (4z + 2w)
We can subtract the polynomial with the different variable to get:
2x + 3y - 4z - 2w
Q: How do I subtract a polynomial with a negative coefficient from a polynomial with a positive coefficient?
A: When we subtract a polynomial with a negative coefficient from a polynomial with a positive coefficient, we need to distribute the negative sign to all the terms in the polynomial. For example, if we have:
2x + 3y - (-4x - 2y)
We can distribute the negative sign to get:
2x + 3y + 4x + 2y
Q: Can I subtract a polynomial from a polynomial with a different degree?
A: Yes, you can subtract a polynomial from a polynomial with a different degree. However, you need to make sure that the terms with the same degree are combined correctly. For example, if we have:
x^2 + 2x - (3x + 4)
We can subtract the polynomial with the different degree to get:
x^2 + 2x - 3x - 4
Q: How do I check my answer when subtracting polynomials?
A: When subtracting polynomials, it's essential to check your answer by plugging in some values for the variables. This will help you ensure that your answer is correct. For example, if we have:
x^2 + 2x - (3x + 4)
We can plug in x = 1 to get:
(1)^2 + 2(1) - (3(1) + 4) = 1 + 2 - 7 = -4
This confirms that our answer is correct.
Conclusion
In this article, we answered some of the most frequently asked questions about subtracting polynomials. We covered topics such as subtracting polynomials with different variables, subtracting polynomials with negative coefficients, and checking our answers. By following these tips and techniques, you can become more confident in your ability to subtract polynomials.
Additional Resources
If you want to learn more about subtracting polynomials, we recommend checking out the following resources:
- Khan Academy: Subtracting Polynomials
- Mathway: Subtracting Polynomials
- Wolfram Alpha: Subtracting Polynomials
These resources provide additional examples, explanations, and practice problems to help you master the concept of subtracting polynomials.