Problem on Factorization

Topic : Factorization

Problem : Solve a^4 +3a^3+27a+81

Solution :
a^4 +3a^3+27a+81
First let's group the terms
(a^4 +3a^3)+(27a+81)
Now we take common factors
from each parenthesis.
a^3(a+3)+ 27(a+3) as 81/27 = 3
Again we have a common factor
(a+3)
So, (a+3)(a^3+27)
or (a+3)(a^3+3^3)
Applying the formula x^3+y^3 = (x+y)(x^2-xy+y^2) for a^3+b^3
we get (a+3)(a+3)(a^2-3a+3^2)
(a+3)(a+3)(a^2-3a+9)
or
(a+3)^2(a^2-3a+9)