I am having real trouble getting to the corrects answers when asked to simply Sum of products expressions. For instance:
Determine whether the left and right hand sides represent the same function:
a) $x_1\bar{x}_3+x_2x_3+\bar{x}_2\bar{x}_3 = (x_1+\bar{x}_2+x_3)(x_1+x_2+\bar{x}_3)(\bar{x}_1+x_2+\bar{x}_3)$
They answer is that they are equivalent. Here is my logic for solving the left hand side, I first expand so each term has 3 variables:
$=x_1x_2\bar{x}_3+x_1\bar{x}_2\bar{x}_3+x_1x_2x_3+\bar{x}_1x_2x_3+x_1\bar{x}_2\bar{x}_3+\bar{x}_1\bar{x}_2\bar{x}_3$
combining terms
$\begin{align*} &=x_1x_2(\bar{x}_3+x_3)+(x_1+\bar{x}_1)\bar{x}_2\bar{x}_3+x_1\bar{x}_2\bar{x}_3\\ &=x_1x_2+\bar{x}_2\bar{x}_3+x_1\bar{x}_2\bar{x}_3 \end{align*}$
Then if I apply De Morgan's law in order to get it in Product of sum form, I get nothing close to the equivalent of the right hand side.