Japan Junior Mathematical Olympiad

Question

Calculate the following number: 877 879 - 121 123.

Accepted Answer

Using (a-b)(a+b) = a^2-b^2, we obtain aligned 877 879 - 121 123 &= (878 - 1)(878 + 1) - (122 - 1)(122 + 1) &= (878^2 - 1) - (122^2 - 1) = 878^2 - 122^2 &= (878 - 122)(878 + 122) = 756 1000 = 756000. aligned Alternatively, aligned 877 879 - 121 123 &= 877 (1000 - 121) - 121 123 &= 877 1000 - 121 (877 + 123) &= 877 1000 - 121 1000 = 756000. aligned