The polynomial is a difference squares. use the formula a^2 -b^2=(a+b)(a-b) to factor completely. 81x^2-49 the value of a is the value of b is the product of the prime factors is

Step-by-step explanation:

1. By definition you have that the difference of squares is:

2. Given the polynomial:

You can identify that there are two terms whose signs are different and they are perfect squares.

3. Therefore, you have:

 

The balloon rocketed into the sky.   Though we were frightened, everything ended up being fine.

The word "quickly" can be removed because speed is implied with the word "rocketed"The phrase "into the really cold air" can be removed because it is irrelevant to what's happening.  It can be replaced by "into the sky"Now "up" can be removed because "into the sky" implies that the balloon went upwards.Either the word "scared" or "frightened" can be removed because they're synonyms (I chose to remove "scared")"Because it was moving really fast" can be removed because the use of the word "rocketed" beforehand already implies that the balloon was moving fast.Lastly , I just reworded and conjoined some of the sentences to make them read more clearly though this isn't necessary. (I changed the third sentence from "However, it was all good in the end," to "everything ended up being fine." I also combined the second and third sentences, adding "though" in front of the second sentence to make it a dependent clause)