1. ## symbols as variables

The question is:

For all positive integers x, let x▲ be defined to be (x-1)(x+1). Which of the following is equal to 6▲-5▲?
A) 2▲ +1▲
B) 3▲+2▲
C) 4▲+3▲
D) 5▲+4▲
E) 6▲+5▲

I was under the impression that if I substituted (x-1)(x+1) for ▲ and worked the problem, I could come up with the answer, but I must be missing something. I am aware that the minus sign in the original problem is the subtraction of a binomial, but that did not help.

2. ## Re: symbols as variables

Originally Posted by klg
The question is:

For all positive integers x, let x▲ be defined to be (x-1)(x+1). Which of the following is equal to 6▲-5▲?
A) 2▲ +1▲
B) 3▲+2▲
C) 4▲+3▲
D) 5▲+4▲
E) 6▲+5▲
The easy way to answer this is to note that $(x-1)(x+1)=x^2-1$.
So $6\blacktriangle=36-1=35.$

3. ## Re: symbols as variables

Thank you, for some reason I thought it was more difficult.