Algebra and Finding a Formula: Connecting N (or Size) with Difference

[Lukeitfc]

I know it's easy to all you people, but my first question is, is this right:

Difference between ( X) x (X+21) and (X+1) x (X+20)=20
=(x²+x+20x+20)-(x²+21x)
=(x²+21x+20)-(x²+21x)
=(21x+20)-21x
=20

I think it is, that's one point

Point 2
I just can't find an expression which connects N(or Size) with Difference

N Size Difference
1 2x2 40
2 3x3 160
3 4x4 240
4 5x5 640




Thanks In Advance

 

[Tom McCurdy]

I am not sure what you are asking about with the N difference... what exactly are you solving for?

 

[Diane_]

I know it's easy to all you people, but my first question is, is this right:

Difference between ( X) x (X+21) and (X+1) x (X+20)=20
=(x²+x+20x+20)-(x²+21x)
=(x²+21x+20)-(x²+21x)
=(21x+20)-21x
=20


Well, the first one resolves to x^2 + 21x. It's an expression, not an equation, so it can't be "solved" per se - just simplified or rewritten.

The second is an equation - trite though it may sound, it has an "equals" sign. The left side of the second is clearly not equivalent to the first. Think of it like this: let x have a value, say 10. The first, then, would be the same as

(x)(x + 21) = 10 * 31 = 310

The second would be

(x + 1)(x + 20) = 11 * 30 = 330

Clearly not the same.

Does that answer your question? If not, could you be a little more specific? (Gee, I'm saying that a lot tonight...)