# How do you factor completely: 42x^3y^4 - 63x^2y?

$42 {x}^{3} {y}^{4} - 63 {x}^{2} y = 21 {x}^{2} y \left(2 x {y}^{3} - 3\right)$
The highest common factor of the terms is $21 {x}^{2} y$, so separate that out as a factor to get:
$42 {x}^{3} {y}^{4} - 63 {x}^{2} y = 21 {x}^{2} y \left(2 x {y}^{3} - 3\right)$
The remaining factor $\left(2 x {y}^{3} - 3\right)$ does not factorise further.