Answer
$17xy^{3}(y+3x)$
Work Step by Step
List the prime factors of each term. Identify the factors common to all terms.
$17xy^{4}=(17)\cdot(x)\cdot(y\cdot y\cdot y)\cdot y$
$51x^{2}y^{3}=3\cdot(17)\cdot(x)\cdot x\cdot(y\cdot y\cdot y)$
GCF= $17xy^{3}$
$17xy^{4}+51x^{2}y^{3}\qquad...$factor out the GCF
$=17xy^{3}(y)+17xy^{3}(3x)\qquad...$apply the Distributive Property.
$=17xy^{3}(y+3x)$
