Why do you need to find a least common denominator before you can add or subtract fractions with unlike denominator?

Because having a common denominator means that you can perform functions on the fractions as if they were 'normal' (by that I mean integer) numbers. You can't subtract 1/8 from 1/4 because their denominators make them completely different numbers. However making the denominators of both 8, by multiplying the numerator anf denominator of the first fraction by 2, gives you 2/8 - 1/8, which can be done. As much as I'd love to give you an analogy for it, I can't think of one, so you just kind of have to take my/the teacher's word for it

The monomial x would be the length of the sports banner.

-We know this because we typically use a basic variable for the thing that does not change. In this case, the length of the sports banner remains the same.

The second degree term in the expression would be the increase in area of the culture banner to make the sports banner.

-We can tell this because when we increase the width of the banner by 12, the resulting polynomial is 12x larger than x^2 (which was the original area of the culture banner.

The binomial expression x + 12 would be the width of the sports banner.

-Since we are increasing the width of the culture banner from x, x + 12 would represent the new width of the sports banner.

The first degree term in the expression would be the area of the culture banner.

-Because side of the culture banner is the same before the increase, multiplying x by itself will give you an area of x^2. This is the first degree term.