how to compare the large numbers without using calculator and/or without large calculation

Question

for the given two multiplication below, what is the relationship (>,< or =) .. between this two multiplication?

100210*90021 and 
100021*90210

I can simply compare these two results by calculation of multiplication but it is too time-consuming and not an effective way of solving this type of questions. I want different way of finding the relationship (>,< or =) ..

Answer 1

Note that

$$100210 \cdot90021=(100021+189)(90210-189)=\\=100021\cdot90210+189\cdot 90220-189\cdot 100021$$

Answer 2

In $100210\cdot 90021,$ you multiply $210$ by $90000$ and $21$ by $100000$.

In $100021\cdot09210,$ you multiply $210$ by $100000$ and $21$ by $90000$.

The second one is larger.