Answer
$3yz^3\left( 5y^{2}-9yz+1 \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Get the $GCF$ of each term of the given expression, $
15y^3z^3-27y^2z^4+3yz^3
.$ Divide the given expression and the $GCF.$ Express the answer as the product of the $GCF$ and the resulting quotient.
$\bf{\text{Solution Details:}}$
Using the $GCF=
3yz^3
,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
3yz^3\left( \dfrac{15y^3z^3}{3yz^3}-\dfrac{27y^2z^4}{3yz^3}+\dfrac{3yz^3}{3yz^3}
\right)
.\end{array}
Using the Quotient Rule of the laws of exponents which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the expression above simplifies to
\begin{array}{l}\require{cancel}
3yz^3\left( 5y^{3-1}z^{3-3}-9y^{2-1}z^{4-3}+y^{1-1}z^{3-3}
\right)
\\\\=
3yz^3\left( 5y^{2}z^{0}-9y^{1}z^{1}+y^{0}z^{0}
\right)
\\\\=
3yz^3\left( 5y^{2}(1)-9yz+1(1)
\right)
\\\\=
3yz^3\left( 5y^{2}-9yz+1 \right)
.\end{array}
