Which Shows Two Expressions That Are Equivalent To $(-8)(-12)(2)$?A. $(-96)(2)$ And \$(-8)(-24)$[/tex\]B. $(-8)(-24)$ And $(-1)(192)$C. \$(-96)(2)$[/tex\] And
When dealing with mathematical expressions, it's essential to understand the concept of equivalent expressions. Equivalent expressions are those that have the same value, even if they are written differently. In this article, we will explore the concept of equivalent expressions and determine which two expressions are equivalent to $(-8)(-12)(2)$.
Understanding the Concept of Equivalent Expressions
Equivalent expressions are expressions that have the same value, even if they are written differently. This means that if we have two expressions, and we can simplify them to the same value, then they are equivalent. For example, the expressions $2 \times 3$ and $6$ are equivalent because they both have the same value.
Simplifying the Given Expression
To determine which two expressions are equivalent to $(-8)(-12)(2)$, we need to simplify the given expression. We can start by multiplying the first two numbers, $-8$ and $-12$.
Now, we can multiply the result by the third number, $2$.
So, the simplified expression is $192$.
Analyzing the Options
Now that we have simplified the given expression, we can analyze the options to determine which two expressions are equivalent to $192$.
Option A: $(-96)(2)$ and $(-8)(-24)$
Let's start by analyzing the first expression in Option A, $(-96)(2)$. We can simplify this expression by multiplying $-96$ by $2$.
This expression is not equivalent to $192$, so we can eliminate Option A.
Option B: $(-8)(-24)$ and $(-1)(192)$
Now, let's analyze the first expression in Option B, $(-8)(-24)$. We can simplify this expression by multiplying $-8$ by $-24$.
This expression is equivalent to $192$, so we can keep Option B as a possible solution.
Option C: $(-96)(2)$ and $(-1)(192)$
We have already analyzed the first expression in Option C, $(-96)(2)$. We found that it is not equivalent to $192$, so we can eliminate Option C.
Conclusion
Based on our analysis, we can conclude that the two expressions that are equivalent to $(-8)(-12)(2)$ are $(-8)(-24)$ and $(-1)(192)$. These expressions have the same value, $192$, and are therefore equivalent.
Key Takeaways
- Equivalent expressions are those that have the same value, even if they are written differently.
- To determine which two expressions are equivalent to a given expression, we need to simplify the given expression.
- We can analyze the options by simplifying each expression and determining if it is equivalent to the given expression.
Final Answer
In our previous article, we explored the concept of equivalent expressions and determined which two expressions are equivalent to $(-8)(-12)(2)$. In this article, we will answer some frequently asked questions about equivalent expressions.
Q: What is the difference between equivalent expressions and equivalent equations?
A: Equivalent expressions and equivalent equations are related concepts, but they are not the same thing. Equivalent expressions are expressions that have the same value, even if they are written differently. Equivalent equations, on the other hand, are equations that have the same solution, even if they are written differently.
Q: How do I determine if two expressions are equivalent?
A: To determine if two expressions are equivalent, you need to simplify each expression and determine if they have the same value. You can use various mathematical operations, such as addition, subtraction, multiplication, and division, to simplify the expressions.
Q: What are some common mistakes to avoid when working with equivalent expressions?
A: Some common mistakes to avoid when working with equivalent expressions include:
- Not simplifying the expressions enough
- Not checking if the expressions have the same value
- Not considering the order of operations
- Not using the correct mathematical operations
Q: Can equivalent expressions have different variables?
A: Yes, equivalent expressions can have different variables. For example, the expressions $2x$ and $4y$ are equivalent if $x = 2y$.
Q: Can equivalent expressions have different coefficients?
A: Yes, equivalent expressions can have different coefficients. For example, the expressions $3x$ and $6y$ are equivalent if $x = 2y$.
Q: How do I use equivalent expressions in real-world problems?
A: Equivalent expressions can be used in a variety of real-world problems, such as:
- Simplifying complex mathematical expressions
- Solving equations and inequalities
- Modeling real-world situations
- Making predictions and forecasts
Q: Can equivalent expressions be used in algebraic manipulations?
A: Yes, equivalent expressions can be used in algebraic manipulations, such as:
- Factoring expressions
- Expanding expressions
- Canceling common factors
- Simplifying expressions
Q: Are equivalent expressions always true?
A: No, equivalent expressions are not always true. If two expressions are equivalent, it means that they have the same value, but it does not mean that they are always true. For example, the expressions $x = 2$ and $x = 3$ are not equivalent, even though they are both true.
Conclusion
In this article, we answered some frequently asked questions about equivalent expressions. We discussed the difference between equivalent expressions and equivalent equations, how to determine if two expressions are equivalent, and some common mistakes to avoid when working with equivalent expressions. We also explored how equivalent expressions can be used in real-world problems and in algebraic manipulations.
Key Takeaways
- Equivalent expressions are expressions that have the same value, even if they are written differently.
- To determine if two expressions are equivalent, you need to simplify each expression and determine if they have the same value.
- Equivalent expressions can have different variables and coefficients.
- Equivalent expressions can be used in a variety of real-world problems and in algebraic manipulations.
Final Answer
The final answer is: