Is there any way to mate the opponent when with a bishop and knight.
Yes. Just move the Bishop to f3. Get the king to a corner of the same color as the bishop.
how can you forcibly move a king into the corner with a knight and bidhop
http://en.wikipedia.org/wiki/Bishop_and_knight_checkmate
There is also a puzzle in the More Puzzles that does the knight+bishop mate.
There happens to be an excellent article here on chess.com covering this very topic...
http://www.chess.com/article/view/how-to-checkmate-with-king-bi
It is one of the most technically difficult checkmates to achieve (remember, you only have 50 moves). You have to be very precise. One mistake and the King will slip away. If he slips away at move 42, there's no way you'll get him back in time. Read the article. It's well-written.
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