Partial grouping with four terms

Example — Factorise $6a^4b + 3a^2c + 2a^2b^2 + bc$

I group the four terms into two pairs and look for the common factor of each.

In each pair the overlap contains the common factor ($3a^2$ and $b$); the remainders ($2a^2b$ and $c$) form the common binomial $(2a^2b+c)$.

Therefore $6a^4b + 3a^2c + 2a^2b^2 + bc = \boxed{(2a^2b+c)(3a^2+b)}$.

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Topics: Algebraic calculation
Concepts: Partial grouping · Factorisation
Skills: Factorising