Answer
$\color{blue}{35(5t+3)^{-5/3}(-5t-2)(3t+2))}$
Work Step by Step
The least exponent of the binomials is $-5/3$.
The numerical coefficients have a greatest factor of $7$.
Factor out $7(5t+3)^{-5/3}$ to obtain:
$=7(5t+3)^{-5/3}[1+2(5t+3)-3(5t+3)^{2}]$
Distribute $2$ to obtain:
$\\=7(5t+3)^{-5/3}[1+10t+6-3(5t+3)^{2}]
\\=7(5t+3)^{-5/3}[10t+7-3(5t+3)^{2}]$
Square the binomial to obtain:
$\\=7(5t+3)^{-5/3}[10t+7-3(25t^2+30t+9)]$
Distribute $3$ then combine like terms to obtain:
$=7(5t+3)^{-5/3}(10t+7-75t^2-90t-27)
\\=7(5t+3)^{-5/3}(-75t^2-80t-20)$
Factor out $5$ in the trinomial to obtain:
$\\=7(5t+3)^{-5/3}\cdot 5(-15t^2-16t-4)
\\=35(5t+3)^{-5/3}(-15t^2-16t-4)$
Factor the trinomial to obtain:
$=\color{blue}{35(5t+3)^{-5/3}(-5t-2)(3t+2))}$
