Factor the expression 8x3y - 8x2y - 30xy.

8x3y - 8x2y - 30xy

2xy (2x + 3) (2x - 5)

Step-by-step explanation:

The greatest common factor of the coefficients 8 and 30 is 2. All of the variable expressions have a common factor of xy. We can factor those out to get ...

= (2xy) (4x^2 - 4x - 15)

Now, we want to find factors of the product (4) (-15) that have a sum of - 4 (the x coefficient). Those factors are 6 and - 10. Then we can rewrite the quadratic factor as ...

4x^2 + 6x - 10x - 15

and factor by pairs:

= 2x (2x + 3) - 5 (2x + 3) = (2x - 5) (2x + 3)

The complete factorization is then ...

= 2xy (2x + 3) (2x - 5)