The sum of products expansion is easily obtained from the truth table. For each line of the table where the function value is 1, e.g.,
you add one product to the sum. In this product, you write is the 's column has 1, and if the 's column has 0. (I assumed that the negation of is denoted ; you may have a different notation.) Also, you do the same for . So, for the line above, you add the following product: .
x | y | F(x,y)
1 | 0 | 1
To repeat, you add all such products for lines where .