Answer
17x$y^{3}$(y+3x)
Work Step by Step
17x$y^{4}$+51$x^{2}$$y^{3}$
Prime factors of each term are:
17$\times$x$\times$y$\times$y$\times$y$\times$y
17$\times$3$\times$x$\times$x$\times$y$\times$y$\times$y
Thus, the GCF is : $17xy^{3}$
The second term can be written as: $17xy^{3}(y+3x)$