How do you factor by grouping 35xy5x56y+8?

3 Answers
May 10, 2015

Notice that 355=7 and 568=7, so we will do well to group as follows:

35xy5x56y+8=(35xy5x)(56y8)
=5x(7y1)8(7y1)
=(5x8)(7y1).

May 10, 2015

First note that the first group of two terms have a common factor of 5x, so 35xy5x56y+8=5x(7y1)56y+8. Next, factor 8 out of the second group of two terms to get 5x(7y1)8(7y1). Now both of these terms have a factor of (7y1) that can be factored out. The final answer is 35xy5x56y+8=(7y1)(5x8).

May 10, 2015

Note that the ratio between the first two coefficients (35:5) is the same as the ratio between the last two coefficients (56:8).
This gives us a hint as to a possible solution. (note that at this point it is only "possible"; it is not guaranteed).

(35xy5x)(56y8)

=(5x)(7y1)(8)(7y1)

=(5x8)(7y1)