x³ - 49xy²

The smallest power of a letter that appears in both terms is x

So we factor it out:

x(x² - 49y²)

The parentheses contains the difference of two squares and can be 
written this way:

x[(x)² - (7y)²]

Then the bracketed expression can be factored (or as you say "factorised")
as the product of the difference and the sum of the square roots:

x[(x - 7y)(x + 7y)]

And we don't need the brackets anymore.

x(x - 7y)(x + 7y)

Edwin