Question: factor 3x^4+18x^3+27x^2 completely.
The first (common) factor we can take out is x^2.
x^2(3x^2+18x+27) -- now take out a common factor of 3
3x^2(x^2 + 6x + 9) -- and the quadratic inside the bracket is just a simple square.
3x^2(x + 3)^2
Answer: 3x^2(x + 3)^2