Answer
$\color{blue}{6(3x+1)^{-3/2}(9x^2+8x+2)}$
Work Step by Step
The least exponent of the binomials is $-3/2$.
The numerical coefficients have a greatest factor of $2$.
Factor out $2(3x+1)^{-3/2}$ to obtain:
$=2(3x+1)^{-3/2}[1+2(3x+1)+3(3x+1)^{2}]
\\=2(3x+1)^{-3/2}[1+6x+2+(3x+1)^{2}]
\\=2(3x+1)^{-3/2}[6x+3+(3x+1)^{2}]$
Square the binomial to obtain:
$\\=2(3x+1)^{-3/2}[6x+3+3(9x^2+6x+1)]$
Distribute $3$ then combine like terms to obtain:
$=2(3x+1)^{-3/2}(6x+3+27x^2+18x+3)
\\=2(3x+1)^{-3/2}(27x^2+24x+6)$
Factor out $3$ in the trinomial to obtain:
$\\=2(3x+1)^{-3/2}\cdot 3(9x^2+8x+2)
\\=\color{blue}{6(3x+1)^{-3/2}(9x^2+8x+2)}$
