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Common factors

Double common factors

Example 4

ax + ay + bx + by = a(x+y) + b(x+y) = (x+y)(a+b)

Example 5

In associating the terms in pairs, we see that 3a² is a common factor of the first two terms, and that ab² is a common factor of the last two terms:
3a³+6a²b+a²b²+2ab³ = (3a³+6a²b) + (a²b²+2ab³)

Bringing out these common factors we thus obtain a sum of two terms, which in turn have a common factor of (a+2b).
= 3a² (a+2b)+ab² (a+2b) = (a+2b)(3a²+ab²)

Before proceeding to the exercises, ensure that you have a pencil and some paper handy.