Factor the given expressions by grouping as illustrated in Example 10.

S³ − 5S² − S + 5

Data from Example 10

Factor: 2x − 2y + ax − ay.

We see that there is no common factor to all four terms, but that each of the first two terms contains a factor of 2, and each of the third and fourth terms contains a factor of a. Grouping terms this way and then factoring each group, we have 

2x - 2y + ax - ay = (2x - 2y) + (ax - ay) = 2(x - y) + a(x - y) = (x - y)(2 + a)