Which Expression Can Be Used To Find The Difference Of The Polynomials?A. \[$(10m - 6) - (7m - 4)\$\]B. \[$[-10m + (-7m)] + [(-6) + 4]\$\]C. \[$(10m + 7m) + [(-6) + (-4)]\$\]D. \[$[(-10m) + (-7m)] + (6 + 4)\$\]E.
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 is a fundamental operation in algebra. 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 the Difference of Polynomials?
The difference of two polynomials is a new polynomial that results from subtracting one polynomial from another. This operation is denoted by the subtraction symbol (-) and is used to find the difference between two polynomials.
Example: Finding the Difference of Two Polynomials
Let's consider two polynomials:
P(x) = 10x - 6 Q(x) = 7x - 4
To find the difference of these two polynomials, we need to subtract Q(x) from P(x):
P(x) - Q(x) = (10x - 6) - (7x - 4)
Which Expression Can Be Used to Find the Difference of the Polynomials?
Now, let's examine the given options and determine which one can be used to find the difference of the polynomials:
A. {(10m - 6) - (7m - 4)$}$
B. {[-10m + (-7m)] + [(-6) + 4]$}$
C. {(10m + 7m) + [(-6) + (-4)]$}$
D. {[(-10m) + (-7m)] + (6 + 4)$}$
E.
To find the correct expression, we need to apply the distributive property and combine like terms.
Applying the Distributive Property
The distributive property states that for any real numbers a, b, and c:
a(b + c) = ab + ac
Using this property, we can rewrite the expression in option A as:
(10m - 6) - (7m - 4) = 10m - 6 - 7m + 4
Now, let's combine like terms:
10m - 6 - 7m + 4 = (10m - 7m) + (-6 + 4)
Simplifying further, we get:
3m - 2
Comparing the Options
Now, let's compare the simplified expression with the given options:
A. {(10m - 6) - (7m - 4)$}$
B. {[-10m + (-7m)] + [(-6) + 4]$}$
C. {(10m + 7m) + [(-6) + (-4)]$}$
D. {[(-10m) + (-7m)] + (6 + 4)$}$
E.
The only option that matches the simplified expression is option A.
Conclusion
In conclusion, the correct expression to find the difference of the polynomials is:
A. {(10m - 6) - (7m - 4)$}$
This expression can be simplified to:
3m - 2
By applying the distributive property and combining like terms, we can find the difference of the polynomials.
Final Answer
Q: What is the difference of polynomials?
A: The difference of two polynomials is a new polynomial that results from subtracting one polynomial from another. This operation is denoted by the subtraction symbol (-) and is used to find the difference between two polynomials.
Q: How do I find the difference of two polynomials?
A: To find the difference of two polynomials, you need to subtract one polynomial from another. This can be done by applying the distributive property and combining like terms.
Q: What is the distributive property?
A: The distributive property states that for any real numbers a, b, and c:
a(b + c) = ab + ac
This property can be used to expand and simplify expressions involving addition and subtraction.
Q: How do I apply the distributive property to find the difference of polynomials?
A: To apply the distributive property, you need to distribute the negative sign to each term inside the parentheses. For example, if you have the expression:
(10m - 6) - (7m - 4)
You can apply the distributive property by distributing the negative sign to each term inside the parentheses:
(10m - 6) - (7m - 4) = 10m - 6 - 7m + 4
Q: How do I combine like terms?
A: To combine like terms, you need to add or subtract the coefficients of the terms with the same variable. For example, if you have the expression:
10m - 6 - 7m + 4
You can combine like terms by adding the coefficients of the terms with the same variable:
10m - 7m = 3m
-6 + 4 = -2
So, the simplified expression is:
3m - 2
Q: What are some common mistakes to avoid when finding the difference of polynomials?
A: Some common mistakes to avoid when finding the difference of polynomials include:
- Not applying the distributive property correctly
- Not combining like terms correctly
- Not simplifying the expression correctly
Q: How do I check my work when finding the difference of polynomials?
A: To check your work, you can:
- Plug in a value for the variable and simplify the expression
- Use a calculator to simplify the expression
- Check your work by comparing it to the original expression
Q: What are some real-world applications of finding the difference of polynomials?
A: Finding the difference of polynomials has many real-world applications, including:
- Calculating the difference between two financial investments
- Finding the difference between two physical quantities, such as distance or time
- Solving problems in physics, engineering, and other fields that involve polynomial equations.
Conclusion
In conclusion, finding the difference of polynomials is a fundamental operation in algebra that has many real-world applications. By applying the distributive property and combining like terms, you can simplify expressions and find the difference between two polynomials. Remember to check your work and avoid common mistakes to ensure accuracy.