What
f /. {a1x -> 20, a1y -> 5, b0x -> 0, b0y -> 0}
shows is that
f == p1 * (alx - 20) + p2 * (aly - 5) + p3 * b0x + p4 * b0y
for some polynomials p1, p2, p3, p4. The polynomials are given by
PolynomialReduce[f, {(a1x - 20), (a1y - 5), b0x, b0y}, Variables[f]]