Explain why the product of two binomials in the form (a+b)(a-b) is a binomial instead of a trinomial

Step-by-step explanation:

The reason for this is that the two middle terms, ba and -ba, cancel one another out, leaving only two terms:  a^2 and b^2.

a and c

for infinitely many solutions we require both left and right sides to be equal

distribute and simplify

a

14 - 8x = 20 - 8x - 6 = 14 - 8x ← both sides equal so infinite solutions

b

6x - 54 = 6x - 54 + x = 7x - 54 ← not equal

c

4x + 16 = 4x + 10 + 6 = 4x + 16 ← both sides equal so infinite solutions

d

5x - 40 + 10 = 5x + 10

5x - 30 = 5x + 10 ← not equal