Prove (x+(y (yx)))
(yx+yx) = xy
One proof among many possible:
(x+(y (yx)))
(yx+yx)
 

by simplification 1 
(x+(y (yx))) y



by DeMorgan's Law 
(x+(y + yx)) y



by simplification 2 
(x+y) y



by simplification 3 
x y


Some common mistakes:
 x y
is not equal to xy
 x yz
is not equal to xyz
 xy is not equal to x+
y
 xy = NOT( x+
y)

Be somewhat careful about how many steps you leave out
 OK: x to x (y + y)
 NOT OK: x to x(((y+z)(y+z))+y)
 Some people used the “multiply it all out” approach. That gets cumbersome for bigger proofs.