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