This is one of the questions on the semester exam, which is: Which algebraic expression represents the following phrase? 'The square of the sum of t and 6.'
A. t^2 + 6
B. t + 6^2
C. (t + 6)^2
D. 2(t + 6)
I do believe it is C, but I am not sure.
Yes, you are correct
Thanks, can you help me with more?
To determine which algebraic expression represents the phrase "The square of the sum of t and 6," we need to break it down into parts and analyze each component.
The phrase mentions the sum of t and 6, which can be represented as t + 6. Next, the phrase states that this sum is squared, which means we need to multiply it by itself.
If we multiply (t + 6) by itself, we get (t + 6) * (t + 6). Expanding this expression gives us t^2 + 6t + 6t + 36.
Simplifying the terms, we have t^2 + 12t + 36.
Comparing the options given:
A. t^2 + 6 - This expression does not include the addition of t and 6, nor does it square their sum, so it does not represent the given phrase.
B. t + 6^2 - This expression squares 6, but it does not represent the sum of t and 6, so it also does not match the given phrase.
C. (t + 6)^2 - This expression represents the sum of t and 6, squared. It matches the given phrase, so it is a possible answer.
D. 2(t + 6) - This expression represents twice the sum of t and 6, but it does not square their sum, so it does not match the given phrase.
Therefore, the correct answer is C. (t + 6)^2.