Understanding the Problem
To find the product of 78 × 82, we can use the identity of the difference of squares. This approach simplifies the multiplication and makes calculations easier.
Using the Identity
The identity we will use is:
(a - b)(a + b) = a^2 - b^2
In this case, we can represent 78 and 82 in a suitable form:
- Let a = 80 (the average of 78 and 82)
- Let b = 2 (the difference from 80)
Now we can express 78 and 82 as follows:
- 78 = 80 - 2
- 82 = 80 + 2
Applying the Identity
Now we can apply the difference of squares identity:
- 78 × 82 = (80 - 2)(80 + 2)
Using the identity:
- This equals 80^2 - 2^2
Calculating the Squares
Now we need to calculate the squares:
- 80^2 = 6400
- 2^2 = 4
So, we can substitute these values back into the equation:
- 78 × 82 = 6400 - 4
Final Calculation
Now, subtract:
- 6400 - 4 = 6396
Conclusion
Thus, the product of 78 × 82 is:
- 6396
This method not only provides the answer quickly but also reinforces the understanding of mathematical identities.

78×82
=(80-2)(80+2)
=80² - 2²
=6400-4
=6396 Ans.