Answer
$3x^{2}(x+1 )^{2}$
Work Step by Step
Factor out the greatest common factor, which is, $3x^{2}$:
$3x^4+6x^3+3x^2=3x^{2}(x^{2}+2x+1)$
Recall that: $a^{2}+2ab+b^{2}=(a+b)^2$
The trinomial factor can be written as $x^2+2(x)(1)+1^2$ so using the formula above gives
$x^2+2x+1=(x+1)^2$.
Thus, we have: $3x^{2}(x^{2}+2x+1)= 3x^{2}(x+1 )^{2}$
Therefore, the completely factored form of the given expression is:
$$3x^2(x+1)^2$$
