I'm a bit stuck on one part of Bézout's identity when used with Euclid's algorithm.
The specific part of the equation I can't see is;
3=27-4*(60-2*27)
Which reduces to
3=927-460
(How and why should we know to reduce the equation in this format?)
Then we backward substitute again to say
3=9*(207-3*60)-4*60
Which reduces to
3=9x207-31*60
(Again, how and why do we reduce the equation in this manner?)
This is to satisfy the equation av+bw=d.
Many thanks!