showing Boolean algebra equality

Question

I have this exercise in my worksheet :

Show that x (z ⊕ y) = xz ⊕ xy

I reached this in solving it , but didn't reach the final equation
x(z'y + zy')
xz'y + xzy'
please can someone show how

Answer 1

The truth table shows that both expressions are in fact equivalent:

Answer 2

Checking the above expression with the truth table is the best option. There is another crude way to prove the same.

xz ⊕ xy = xz (xy)' +(xz) 'xy

      = xz (x'+ y') + (x'+ z') xy
      = xx'z + xzy' + x'xy + xyz'       xx'=0 and yy'=0
      = xzy' + xyz'
      = x ( zy' + yz')
      = x (y ⊕ z)