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)

answer: 2 and 1

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