Simplify X² + 1 X 1: Easy Steps To Understand
Table of Contents :
To simplify the expression ( x² + 1 \times 1 ), we need to follow some straightforward steps that will help clarify the process. Understanding the order of operations and the basic arithmetic involved is crucial for a smooth simplification. Let’s break it down!
Understanding the Expression
First, let’s take a closer look at the expression we want to simplify:
The Expression: ( x² + 1 \times 1 )
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What does ( x² ) mean?
- ( x² ) represents ( x ) multiplied by itself. For instance, if ( x = 2 ), then ( x² = 4 ).
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What does ( 1 \times 1 ) mean?
- ( 1 \times 1 ) simply equals 1. This multiplication doesn't change the value of the expression.
Order of Operations
It is important to remember the order of operations (often remembered by the acronym PEMDAS):
- P: Parentheses
- E: Exponents
- MD: Multiplication and Division (from left to right)
- AS: Addition and Subtraction (from left to right)
In our expression, since there are no parentheses or exponents outside of the ( x² ), we should first perform the multiplication ( 1 \times 1 ).
Step-by-Step Simplification
Let’s go through the steps to simplify ( x² + 1 \times 1 ).
Step 1: Perform the Multiplication
Calculate ( 1 \times 1 ):
[ 1 \times 1 = 1 ]
Step 2: Substitute Back into the Expression
Now, substitute this result back into the expression:
[ x² + 1 ]
Step 3: Final Expression
Since we cannot combine ( x² ) and ( 1 ) further (as they are not like terms), the simplified form of the expression is:
[ x² + 1 ]
Key Takeaways
- Simple Operations: We learned that simplifying expressions involves following the order of operations carefully.
- Understanding Terms: Recognizing what each term means in the expression helps in the simplification process.
- Final Form: The final simplified form of ( x² + 1 \times 1 ) is ( x² + 1 ).
Example Scenarios
To further understand, let’s look at a few values of ( x ):
| Value of ( x ) | Value of ( x² + 1 ) |
|---|---|
| 0 | ( 0² + 1 = 0 + 1 = 1 ) |
| 1 | ( 1² + 1 = 1 + 1 = 2 ) |
| 2 | ( 2² + 1 = 4 + 1 = 5 ) |
| 3 | ( 3² + 1 = 9 + 1 = 10 ) |
As you can see from the table, depending on the value of ( x ), the expression yields different results while always maintaining the form ( x² + 1 ).
Important Notes
"Remember to always apply the order of operations correctly to avoid mistakes when simplifying expressions!"
By grasping these concepts and following the outlined steps, you can simplify similar expressions effectively. This foundational understanding can serve as a stepping stone for tackling more complex algebraic problems in the future. 😊