First learn the principle of factorising 
the difference of two squares. Here is 
why it works:

A²-B² = (A-B)(A+B)

Proof: (A-B)(A+B) = A²+AB-AB-B² = A²-B²

So we memorise:

A²-B² is factorized as (A-B)(A+B)

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16x²-25y²

Since 16=4² and 25=5², we can rewrite that as

4²x²-5²y²

and again as

(4x)²-(5y)²

Since we have memorized that

A²-B² is factorised as (A-B)(A+B)

We can substitute 4x for A and 5y for B and get that

(4x)²-(5y)² is factorised as (4x-5y)(4x+5y)

Edwin