First factor the each term in the expression.

100x³ =  2 · 2 · 5 · 5 · x · x · x

75y³ =  5 · 5 · 3 · y · y · y

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

GCF = 5 · 5 = 25

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

100x³  + 75y³ = 25 (4x³) + 25(3y³)

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

100x³  + 75y³ = 25 (4x³ + 3y³)

Simplified expression is 25 (4x³ + 3y³).