%5E2%3D5n%5E2-correct-or-incorrect.jpeg "(5n)^2=5n^2 Correct Or Incorrect")
Is (5n)^2 = 5n^2?
This is a common misconception in algebra, but the equation (5n)^2 = 5n^2 is incorrect. Let's break down why:
Understanding Order of Operations
The order of operations (often remembered by the acronym PEMDAS or BODMAS) dictates the sequence in which we perform calculations:
- Parentheses (or Brackets)
- Exponents (or Orders)
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Applying the Rules
Let's analyze both sides of the equation:
- (5n)^2: This means we square the entire expression inside the parentheses. So, we first multiply 5n by itself: (5n) * (5n) = 25n^2
- 5n^2: Here, we square only the variable 'n', then multiply by 5. This results in 5 * n * n = 5n^2
The Difference
As we can see, (5n)^2 = 25n^2 and 5n^2 are not equal. We need to follow the order of operations and square the entire expression in the parentheses for the left side of the equation.
In Conclusion
The equation (5n)^2 = 5n^2 is incorrect. Remember that squaring an expression inside parentheses applies to all elements within those parentheses, resulting in a different outcome than simply squaring the variable.