The Variables $X, Y,$ And $Z$ Represent Polynomials Where \$X = A,$[/tex\] $Y = 3a - 5,$ And $Z = A^2 + 2.$ What Is \$X^2 Y - Z$[/tex\] In Simplest Form?A. $2a^2 - 5a -
Understanding the Problem
In this problem, we are given three variables, X, Y, and Z, which represent polynomials. The values of these polynomials are defined as follows:
- X = a
- Y = 3a - 5
- Z = a^2 + 2
We are asked to find the value of the expression X^2 Y - Z in its simplest form.
Breaking Down the Expression
To simplify the given expression, we need to follow the order of operations (PEMDAS):
- Evaluate the exponent (X^2)
- Multiply the result by Y
- Subtract Z from the product
Step 1: Evaluate the Exponent (X^2)
The first step is to evaluate the exponent X^2. Since X = a, we can substitute the value of X into the expression:
X^2 = a^2
Step 2: Multiply the Result by Y
Next, we multiply the result by Y. We can substitute the value of Y into the expression:
X^2 Y = a^2 (3a - 5)
Using the distributive property, we can expand the expression:
X^2 Y = 3a^3 - 5a^2
Step 3: Subtract Z from the Product
Finally, we subtract Z from the product:
X^2 Y - Z = 3a^3 - 5a^2 - (a^2 + 2)
Simplifying the Expression
To simplify the expression, we can combine like terms:
X^2 Y - Z = 3a^3 - 6a^2 - 2
Conclusion
In this problem, we were given three variables, X, Y, and Z, which represent polynomials. We were asked to find the value of the expression X^2 Y - Z in its simplest form. By following the order of operations and simplifying the expression, we arrived at the final answer:
X^2 Y - Z = 3a^3 - 6a^2 - 2
Final Answer
Understanding the Problem
In this problem, we are given three variables, X, Y, and Z, which represent polynomials. The values of these polynomials are defined as follows:
- X = a
- Y = 3a - 5
- Z = a^2 + 2
We are asked to find the value of the expression X^2 Y - Z in its simplest form.
Breaking Down the Expression
To simplify the given expression, we need to follow the order of operations (PEMDAS):
- Evaluate the exponent (X^2)
- Multiply the result by Y
- Subtract Z from the product
Step 1: Evaluate the Exponent (X^2)
The first step is to evaluate the exponent X^2. Since X = a, we can substitute the value of X into the expression:
X^2 = a^2
Step 2: Multiply the Result by Y
Next, we multiply the result by Y. We can substitute the value of Y into the expression:
X^2 Y = a^2 (3a - 5)
Using the distributive property, we can expand the expression:
X^2 Y = 3a^3 - 5a^2
Step 3: Subtract Z from the Product
Finally, we subtract Z from the product:
X^2 Y - Z = 3a^3 - 5a^2 - (a^2 + 2)
Simplifying the Expression
To simplify the expression, we can combine like terms:
X^2 Y - Z = 3a^3 - 6a^2 - 2
Q&A
Q: What is the value of X in the given expression? A: The value of X is a.
Q: What is the value of Y in the given expression? A: The value of Y is 3a - 5.
Q: What is the value of Z in the given expression? A: The value of Z is a^2 + 2.
Q: How do we simplify the expression X^2 Y - Z? A: To simplify the expression, we need to follow the order of operations (PEMDAS) and combine like terms.
Q: What is the final answer to the expression X^2 Y - Z? A: The final answer is 3a^3 - 6a^2 - 2.
Common Mistakes
- Not following the order of operations (PEMDAS)
- Not combining like terms
- Not substituting the values of X, Y, and Z into the expression
Tips and Tricks
- Make sure to follow the order of operations (PEMDAS)
- Combine like terms to simplify the expression
- Substitute the values of X, Y, and Z into the expression
Conclusion
In this problem, we were given three variables, X, Y, and Z, which represent polynomials. We were asked to find the value of the expression X^2 Y - Z in its simplest form. By following the order of operations and simplifying the expression, we arrived at the final answer:
X^2 Y - Z = 3a^3 - 6a^2 - 2
Final Answer
The final answer is: