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Using Sarus's rule, you get (a+x)(a+y)(a+y)+yzx+zxy-z(z+y)x-yx(a+z)-(a+x)zy, and when you calculate this and take a^2 out, your proof is done:)
Whats Sarus's rule ?
It's a rule for determining a 3x3 determinant. You just write first 2 columns after the third, and add multiplied elements on the diagonals from left to right, and substract multiplied element on the diagonals from right to left.
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