Just because White won doesn't mean that the position is a win for White. The game is a good study.
34 ... e5 is a horrible move for Black; it draws him away from the center and lets White into the Queenside, where his pawn majority will get to the 8th rank sooner than Black's will.
34 ... g5!
35 fxg5 hxg5
36 h3
White wants to create a Kingside passed pawn. 36 g3 g4 stops that.
36 ... f5
Of course, Black isn't going to sit around and wait. Now the sides race to get a Queen. The alternative would be to maneuver their Kings about, which would accomplish nothing for either side.
37 b4 e5
38 a4 f4
39 b5 axb5
40 Kxb5
Weaker is 40 axb5 e4, 41 Kd4 e3, 42 Kd3 Kc5, 42 g3! (if White dawdles with 42 Kf2? he loses to Kxc5, 43 g3 Kc4!, 44 gxf4 fxf4, 45 h4 Kd5, and Black is within the "square" and can stop the h pawn.) fxg3 (or e2 first; Kxc5 is an error now, because after the pawns are exchanged, White can promote his a-pawn) 43 Kxe3 Kxc5, 44 Kf3 g2, 45 Kxg2 Kc5, and Black has time to get back to stop the h pawn.
40 Kxb5 Kd5!
Black must block White's access to the Kingside before threatening to advance his pawns
41 a5 Kd6!
Black needs to get his King off of the long diagonal to prevent White promoting with check, as will be seen in a few moves
42 a6
There are other lines which also lead to draws; this one follows the previous note
42... f3!
42 .. e3? loses because after both sides promote, White can play Qd8+ and Qe8+, winning the Queen.
43 gxf3
And not 43 a7?? which loses tp 43... fxg2, 44 a8=Q g1=Q+, and Black can force the trade of Queens and win.)
43... gxf3
44 a7 f2
45 a8=Q
Now the point of playing 41... Kd6 first is seen: the promotion is without check.
45 ... f1=Q
The Nalimov Tablebase states that this is a draw.
There was a lot of content in that endgame, which made it good one to study.
I'm following Chess Mentor, because the advertisement says it should improve me, but what I find is a lack of professionality in the IM and FM who made the course (Pawn Endings: Beginner to Expert, by IM Eric Tangborn, FM Thomas Wolski).
Yesterday I found a big mistake, and today I found another, in an endgame, and a game which is not new, but played in 1958, and surely analyzed endless times.
What upsets me is that luckily I learned to think in school, where the scientific system asks to question everything, but I doubt the rest of chess.com members will question, and they will end with wrong knowledge.
Here is the example of a game from Tal, that they use as example of pawn endgame. When I saw the position my gut told me: it should be a draw. But the authors wrote that white won. So I tried to learn how white won, and tried to play it against the computer, medium level 1200 something, and I got beaten a couple of times. Then the next step is to put it in Houdini.
And guess what I discover?? For Houdini after 25 minutes it is still a draw. Then I go to another site to recover the pgn of the game, and also there it seems they analyzed the game with Fritz 13 and it is a draw, white doesn't win.
My suggestion to chess.com is to pay someone who is an amateur, like me, to check the chess mentor courses and correct them, because evidently FMs, IMs and GMs for monetary reasons don't have the time to check, and they just copy and paste.
Here the game and the analysis for those interested.
The analysis will be only from the position given in the chess mentor endgame course.