Show how the binomial expansion can be used to solve these without a calculator

a) 268^2-232^2 b) 469*548+469^2 c) (65.1*29.2+65.1*35.9-91.7-26.4+65.3*26.4)/(18.3^2-18.3*5.4)

(edited 6 years ago)

a)The first one was easy as 268=250+18 and 232=250-18
b) The common factor is 469 so I get 469*(548+469-17). However, I haven't used the binomial expansion in this case to get the result. How do I do it then?
c) I have no idea how to do the c) as I just see random numbers there..

Reply 2

ghostwalker

Original post by pgxrcix

b) The common factor is 469 so I get 469*(548+469-17). However, I haven't used the binomial expansion in this case to get the result. How do I do it then?

For b you could combine two parts to start (your original post appears to be incomplete):

So,

469*548+469^2- 17*469

becomes

469^2+ 531*469

And use a similar trick to a)

c) may fall to some similar logic.

Reply 3

pgxrcix

Original post by ghostwalker

469*548+469^2- 17*469

becomes

469^2+ 531*469

What does that form have to do with the binomial theorem? I don't know any formula for a^2+ab. I guess it is easier to do it the way I did. But, I don't see how that connects to the binomial expansion.