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777777777777777^2 - 222222222222223^2=555,555,555,555,554,000,000,000,000,000

 

(14 x 5)  + 4 = 74 - sum of the digits of the answer.

You don't need a powerful calculator to get the answer that Guest gave you.

 

If you remember this from algebra;  a² - b²  =  (a + b)(a - b)

 

then          777777777777777² - 222222222222223² 

 

beomes:  ( 777777777777777 + 222222222222223 ) · ( 777777777777777 - 222222222222223 )

=                                        (  1 000 000 000 000 000 ) · ( 555 555 555 555 554 )

which gives you the digits from Guest's answer.