First factor the each term in the expression.

42x³y =  2 · 3 · 7 · x · x · x · y

70xy² =  2 · 5 · 7 · x · y · y

The GCF is the product of the common prime factors in each term.

GCF = 2 · 7 · x · y = 14xy

Write each term as a product of the GCF and its remaining factors.

42x³y  + 70xy² = 14xy (3x²) + 14xy (5y)

Combine like terms uisng distribuitve property: ab + ac = a(b + c).

42x³y  + 70xy² = 14xy (3x² + 5y)

Simplified expression is 14xy (3x² + 5y).