Factorise $a^{2} + bc + ab + ac$.

Factorise $a^{2} + bc + ab + ac$.
  1. $(a+b)(a+c)$
  2. $(a-b)(a+c)$
  3. $(a+b)(a-c)$
  4. $(a+bc)(a+1)$

Solution

Group as $(a^{2}+ab)+(ac+bc) = a(a+b)+c(a+b) = (a+b)(a+c)$.

Asked in: IMO

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