Fourth example

Summary

Here the distributive law is applied the other way around compared to the previous examples. Consider

$$12 a^3 b^2 - 30 a^4 b c + 18 a^2 b^3 c^2 \,.$$

Since the factor $6 a^2 b$ occurs in all summands, it can be factored out. That is, due to the distributive law one obtains

$$12 a^3 b^2 - 30 a^4 b c + 18 a^2 b^3 c^2 = 6 a^2 b \left(2 a b - 5 a^2 c + 3 b^2 c^2\right).$$