Let's start with the given polynomial: 2x² - 12xy - 32y²
As a first step, we want to regroup 2: = 2(x² - 6xy - 16y²)
Now, we want to re-write the term -6xy in order to be able to perform a partial factoring. In this case, we can write: -6xy = -8xy + 2xy Therefore, the polynomial becomes: = 2(x² - 8xy + 2xy - 16y²)
Now we factorize x within the first two terms and 2y within the last two: = 2[x(x - 8y) + 2y(x - 8y)]
We can now regroup the common term: =2(x - 8y)(x + 2y)
