ttaiwo wrote:

Hi Bunuel,

I have a two part question:

1. How did you know to use a^2 - b^2 ...plus also how come the powers reduced by half when you used difference of squares i.e. from 8!^10 to *8!^5

2. I understand how the tens digit and the units digit will both be zero...and thus how 8!^2 - 38 = 00-38...I just don't know how you get 62...leading to 6*2=12.

Consider easier examples:

1. \(x^{10} - y^{10} = (x^5)^2 - (y^5)^2 = (x^5 - y^5)(x^5 + y^5)\)

2. 100 - 38 = 62.

I should've seen 2....but I've genuinely haven't come across 1. before ...thanks