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**Hello, I juste don't know how this was done it is on the solutionnary of a very long exercise and i am not getting this calculation**

1. Homework Statement

1. Homework Statement

<1,0| a

_{x}

^{+}a

_{y}

^{+}+a

_{x}

^{+}a

_{y}+a

_{x}a

_{y}

^{+}+a

_{x}a

_{y}|0,1> = <1,0|1,0>

## Homework Equations

3. The Attempt at a Solution

We have that |0,1> = a

_{y}

^{+}|0,0>

I don't understand how they did the simplification to get to the <1,0|1,0>, i am missing something

Thanks [/B]