Final Answer:
The correct expression is N² - 225t² - 1k² + 81p² - 40 (Option 1).
Step-by-step explanation:
The given expression is N² - 225t² - 1k² + 81p² - 40. Comparing this with the provided options, we see that Option 1 is the correct expression.
Now, let's break down the expression:
- N²: This represents N squared.
- 225t²: This is equivalent to 225 times t squared.
- 1k²: This represents 1 times k squared.
- 81p²: This is equal to 81 times p squared.
--40: This is a constant term, subtracting 40.
So, the expression correctly represents the square of N minus 225 times the square of t, minus the square of k, plus 81 times the square of p, minus 40. Therefore, the correct answer is Option 1, which matches the given expression.
In conclusion, when dealing with algebraic expressions, it's crucial to carefully compare and analyze each term to arrive at the correct answer. In this case, understanding the components of the expression and comparing them to the options led us to identify Option 1 as the correct representation of N² - 225t² - 1k² + 81p² - 40.