An algebra problem by Michelle Batad

Algebra Level 2

Factor this out completely:

$a (a+1) (a+2) (a+3) + 1$

(a^+2a+3)^2 (a^2+3a+1)^2 (a+1)^2 3a

1 solution

Michelle Batad
Sep 17, 2014

step 1: group (a+3) a & (a+1) (a+2)

          it will look like this:
          a(a+3) (a+1)(a+2) +1

step 2: multiply a (a+3) (a+1) (a+2) +1

          it becomes:
          (a^2+3a) (a^2+3a  +2) +1

step 3: let a^2+3a = x

          (x) (x+2) +1
          x^2+2x +1           -perfect square trinomial
         (x+1)^2

step 4: substitute x by a^2+3a

        (a^2+3a + 1)^2        -final answer!