Visualize a complex mathematical expression. The image consists of two large numbers being multiplied each other and then subtracted by the product of two other large numbers. The numbers have deeply intricate patterns and they form an abstract mesh of lines and curves avoiding the use of actual digits. The background is a soft gradient shifting from dark blue to pale yellow. Please do not include any text.

Evaluate : 20142015×20152014 – 20142014 ×20152015

letx=20142014

then 20142015=x+1
then 20152014=x+10000
then 20152015=x+10001

20142015×20152014-20142014×20152015
=(x+1)(x+10000)-x(x+10001)
= x²+10001x+10000-x²-10001x
= 10000

10000

Well, that's quite a mouthful! Let's break it down step by step.

First, we have 20142015 × 20152014. If we multiply those numbers together, we get a really big number, but I won't bore you with all the digits.

Next, we have 20142014 × 20152015. Again, if we do the math, we end up with another pretty large number. Imagine trying to fit that on your calculator screen!

Now, the fun part: subtracting the second big number from the first big number. This is like taking candy away from a clown. It's a tricky business!

In the end, after doing all the calculations, we end up with a number that is... well, still pretty big. But hey, at least we had some mathematical fun, right?

To evaluate the given expression, let's break it down step by step:

1. Start with the first term: 20142015 × 20152014
- Multiply 20142015 by 20152014 to get the product: 4,062,048,405,361,610

2. Move to the second term: 20142014 × 20152015
- Multiply 20142014 by 20152015 to get the product: 4,062,048,405,119,510

3. Subtract the second product from the first product:
4,062,048,405,361,610 - 4,062,048,405,119,510 = 242,100

Therefore, the evaluation of the given expression is 242,100.

without a calculator...

let a=20142014
then 20142015 = a+1
then 20152015 = a + 1 + 1000 = a+1001
then 20152014 = a+1000
20142015×20152014 – 20142014 ×20152015

= (a+1)(a+1000) - a(a+1001)
= a^2 + 1001a + 1000 - a^2 - 1001a
= 1000