I had never thought about this...

P.S. Are you trying to hit on Drew using a maths theory?

Clo is onto something. Drew would be the one to ask.

a*b + c = c*b - a

A lovely pattern W_L and quite easy to prove.

In fact you were almost there.

All you have to realise is that in your pattern b is the same as a+1 and c is the same as a+2.

Rewrite the left side of your equation as :

a*(a+1) +(a+2)

Expand and you have a*a +a + (a+2) which is a*a +2a +2

Now do the same with the right side:

(a+2)*(a+1) - a

Expand and you have a(a+1) +2(a+1) - a  which is a*a + a + 2a +2 -a which is a*a +2a + 2

Lo and behold , we've just shown that the left side is exactly the same as the right side.

In other words, as long as the three numbers are consecutive your pattern is always true.

Well it's a proof to the following equation: x²+1

Observe:

a= x-1

b= x

c= x+1

So let's substitute the variables in your equation, a*b+c=c*b-a with variables in terms of x.

That gives us: (x-1)(x)+(x+1)=(x+1)(x)-(x-1)

When we simplify: x²+1=x²+1

That was fun!

Edit: Didn't see Palantir's or Graeme's explanations before I posted, which are a far better explanations than my own in my opinion.

Well it's a proof to the following equation: x²+1

 

Observe:

a= x-1

b= x

c= x+1

 

So let's substitute the variables in your equation, a*b+c=c*b-a with variables in terms of x.

 

That gives us: (x-1)(x)+(x+1)=(x+1)(x)-(x-1)

 

When we simplify: x²+1=x²+1

 

 

That was fun!

 

Edit: Didn't see Palantir's or Graeme's explanations before I posted, which are a far better explanations than my own in my opinion.

So I've proven that Left and Right can equal out in perfect harmony, at least in this instance

"Wink" Drew "Wink"

What you have is two equation:

 

n x (n+1) + (n+2)

 

(n+2) x (n+1) - n

 

Both of these simplify to:

 

n x n + 2 x n + 2

 

So, yes, they'll always be equal. Basic mathematics

Put  in the familiar form used in US text books, a^2 + 2ab + b^2  and I forget the name of that equation

Let me just finish the proof:

a x b + c = c x b -a

b= a +1

c= a + 2

Expressed as a

a(a + 1) + a + 2 = (a + 2)(a + 1) - a

a^2 + a + a + 2 = a*2 + a + 2a + 2 -a

a^2 + 2a + 2= a^2 +2a +2

You can also get the answer like this:

The equations as

a×b+c and

c×b-a

As the three are consecutive numbers, their solutions are equal to either

c^2 - 2b or

a^2 + 2b

In third grade, when I found out 9 was a magic number, I was floored. <3