I'm trying to find the Bézout coefficients for $\gcd(68, 92)$, but I'm having trouble simplifying the substitutions from the results of the Euclidean algorithm.
I am currently stuck at: $$4 = 24 - 1 \times (68 - 2 \times 24)$$ How does $(24 - 1)$ distribute when multiplied with $(68 - 2 \times 24)$?
$92=1\cdot 68 + 24$
$68=2\cdot 24 + 20$
$24=1\cdot 20 + 4$
$20=5\cdot 4 + 0$
=> $\gcd(68,92)=4$
=> $\,4=24-1\cdot 20=24-1\cdot (68-2\cdot 24)=3\cdot 24-1\cdot 68$
$ => 4 =3\cdot(92-1\cdot 68)-1\cdot 68=3\cdot 92-4\cdot 68$
Result: $\,\,4=3\cdot 92-4\cdot 68$