user1105: This position is from a game I played.

I played Bxa1. I'm wondering if instead of Bxa1 I played Bxe5 then he might have played fxe5 then I play Bd3+. Is that a better continuation?
I didn't like his pawn on e5 threatening my knight and wasn't able to find a way to get anything out of the position beside his rook, so i decided to play the simpler move, Bxa1 

user70: 1... Bxa1 2. Rxa1 Be4 will remove another piece from the game leaving you a rook up.
1... Be4 is also a possibility since you'd be threatening to win the bishop on g2. If he trades the bishop, you recapture with the knight and now you're threatening the fork on g3 as well as the rook on a1.
I probably prefer the simpler Bxa1. You're already up a piece and a pawn. White has no compensation. There's no reason to complicate things.

user167: In the initial diagram position, Black is already so much material ahead that either 1...Bxa1 or 1...Bxe5 keeps an overwhelming advantage. But 1...Bxa1 is the most straightforward, and in any case White need not allow 2...Bd3+ after 1...Bxe5 2.Nxe5. Black can first kick the knight with 1...b5 before following with 2...Bxe5 to get the ...Bd3+ idea in; that also keeps a huge plus for Black, but still the simple 1...Bxa1 is cleanest.
[Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "*"]
[FEN "3r1rk1/pp2npp1/4pn2/4Nb1p/2Nb1P2/1P4PP/P3K1B1/R4R2 b - - 0 1"]

1...Bxa1 
    ( 1...Bxe5 $6 {Black starts out ahead so much material that this is 
    perfectly fine, but it is not best, and sloppy if nothing else.} 2.
    Nxe5 {Covering d3, so Black cannot pick up the additional exchange via
    ...Bd3+.} 
        ( 2.fxe5 Bd3+ 3.Ke1 Nd7 {Black is winning handily, but won't be up
        a whole rook and pawn immediately as in the main line.} 4.Bxb7 
        Bxc4 5.bxc4 Nxe5 )
    )
    ( 1...b5 {An attempt to improve on the 1...Bxe5 line, but to no avail,
    and still not as good as just snapping off the rook immediately.} 2.
    Ne3 Bxe5 {Black's first move has deprived White of the knight 
    recapture, but we end up in much the same position as after 1...Bxe5 
    2.fxe5 Bd3+ 3.Ke1 anyway.} 3.fxe5 Bd3+ 4.Ke1 Nd7 5.Rf2 Nxe5 )
2.Rxa1 
    {Black is simply up a rook and pawn with an easily winning position.}
*


1105: <p>This position is from a game I played.</p>

<p><img src="https://i.stack.imgur.com/yU4rR.png" alt="enter image description here"></p>

<p>I played <code>Bxa1</code>. I'm wondering if instead of <code>Bxa1</code> I played <code>Bxe5</code> then he might have played <code>fxe5</code> then I play <code>Bd3+</code>. Is that a better continuation?</p>

<p>I didn't like his pawn on e5 threatening my knight and wasn't able to find a way to get anything out of the position beside his rook, so i decided to play the simpler move, <code>Bxa1</code> </p>
 70: <p>1... Bxa1 2. Rxa1 Be4 will remove another piece from the game leaving you a rook up.</p>

<p>1... Be4 is also a possibility since you'd be threatening to win the bishop on g2. If he trades the bishop, you recapture with the knight and now you're threatening the fork on g3 as well as the rook on a1.</p>

<p>I probably prefer the simpler Bxa1. You're already up a piece and a pawn. White has no compensation. There's no reason to complicate things.</p>
 167: <p>In the initial diagram position, Black is already so much material ahead that either <code>1...Bxa1</code> or <code>1...Bxe5</code> keeps an overwhelming advantage. But <code>1...Bxa1</code> is the most straightforward, and in any case White need not allow <code>2...Bd3+</code> after <code>1...Bxe5 2.Nxe5</code>. Black can first kick the knight with <code>1...b5</code> before following with <code>2...Bxe5</code> to get the <code>...Bd3+</code> idea in; that also keeps a huge plus for Black, but still the simple <code>1...Bxa1</code> is cleanest.</p>

<pre><code>[Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "*"]
[FEN "3r1rk1/pp2npp1/4pn2/4Nb1p/2Nb1P2/1P4PP/P3K1B1/R4R2 b - - 0 1"]

1...Bxa1 
    ( 1...Bxe5 $6 {Black starts out ahead so much material that this is 
    perfectly fine, but it is not best, and sloppy if nothing else.} 2.
    Nxe5 {Covering d3, so Black cannot pick up the additional exchange via
    ...Bd3+.} 
        ( 2.fxe5 Bd3+ 3.Ke1 Nd7 {Black is winning handily, but won't be up
        a whole rook and pawn immediately as in the main line.} 4.Bxb7 
        Bxc4 5.bxc4 Nxe5 )
    )
    ( 1...b5 {An attempt to improve on the 1...Bxe5 line, but to no avail,
    and still not as good as just snapping off the rook immediately.} 2.
    Ne3 Bxe5 {Black's first move has deprived White of the knight 
    recapture, but we end up in much the same position as after 1...Bxe5 
    2.fxe5 Bd3+ 3.Ke1 anyway.} 3.fxe5 Bd3+ 4.Ke1 Nd7 5.Rf2 Nxe5 )
2.Rxa1 
    {Black is simply up a rook and pawn with an easily winning position.}
*
</code></pre>
