Evaluate:20142015×20152014-20142014×20152015
My answer is 10,000 after a lot of calculation
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
without any calculation
just noticed I left out a zero
let a=20142014
then 20142015 = a+1
then 20152015 = a + 1 + 10000 = a+10001
then 20152014 = a+10000
20142015×20152014 – 20142014 ×20152015
= (a+1)(a+10000) - a(a+10001)
= a^2 + 10001a + 10000 - a^2 - 10001a
= 10000
without any calculation
You are great Reiny.
To evaluate the expression 20142015×20152014-20142014×20152015, you need to follow the order of operations, which is known as the "BIDMAS" or "PEMDAS" rule. BIDMAS stands for brackets, indices (or exponents), division, multiplication, addition, and subtraction, and is a way to determine the order in which mathematical operations should be performed.
Let's break down the expression step by step:
1. Evaluate the expressions inside the parentheses or brackets, if any. In this case, there are no brackets or parentheses, so we move to the next step.
2. Evaluate any exponents or indices. Again, there are no exponents or indices, so we move forward.
3. Perform multiplication and division from left to right. In our expression, we have two pairs of multiplication: 20142015 × 20152014 and 20142014 × 20152015. We multiply the first pair and then subtract the result from the second pair. Let's calculate:
20142015 × 20152014 = 4,062,476,207,238,110
20142014 × 20152015 = 4,058,595,208,935,110
Now, subtract the first product from the second:
4,058,595,208,935,110 - 4,062,476,207,238,110 = -3,880,998,303,654,136
Therefore, the evaluated value of the expression 20142015 × 20152014 - 20142014 × 20152015 is -3,880,998,303,654,136.