Factoring by Grouping: Factoring in Pairs

Students learn to factor a polynomial that has four terms by grouping the first two terms together and the last two terms together, then factoring out the Greatest Common Factor from each group. For example, to factor ax – ay + cx – cy, the first step is to factor out an "a" from the first two terms, and factor out a "c" from the last two terms, to get a(x – y) + c(x – y). The problem can now be thought of as two terms, each with a Greatest Common Factor of (x – y), so an (x – y) can be factored out, to get (x – y)(a + c).