What is the difference between 3x and X3?? Explain with examples Someone help me, thank you
What is the difference between 3x and X3?? Explain with examples Someone help me, thank you
The Correct Answer and Explanation is:
The expressions 3x and x³ (often typed as X3) are very different in mathematics, and understanding the distinction is crucial.
Correct Answer:
- 3x means “3 times x” — this is multiplication.
- x³ (read as “x cubed”) means “x raised to the power of 3” — this is exponentiation.
Explanation
In algebra, 3x and x³ represent two different operations involving a variable x, and they produce very different results depending on the value of x.
- 3x (Multiplication):
- This means 3 multiplied by x.
- For example, if x = 2, then 3x = 3 × 2 = 6.
- It is a linear expression because the variable x is raised to the power of 1 (implied).
- Graphically, if you plot y = 3x, it’s a straight line with slope 3.
- It grows at a constant rate as x increases.
- x³ (Exponentiation):
- This means x raised to the power of 3, or x × x × x.
- For example, if x = 2, then x³ = 2³ = 2 × 2 × 2 = 8.
- It is a non-linear expression and is called a cubic function.
- Graphically, y = x³ curves upward steeply as x increases.
- The rate of growth is accelerating—it increases much faster than multiplication.
Comparison Example:
Let’s compare both when x = 4:
- 3x = 3 × 4 = 12
- x³ = 4 × 4 × 4 = 64
Clearly, x³ grows much faster than 3x as the value of x increases.
Conclusion:
- 3x is a simple multiplication that grows steadily.
- x³ is exponentiation and grows rapidly.
- These expressions are not interchangeable and have different mathematical meanings and applications.
Always pay attention to the notation—3x ≠ x³.
