How do you factor by grouping 35xy-5x-56y+8?

3 Answers
May 10, 2015

Notice that 35/5 = 7 and 56/8 = 7, so we will do well to group as follows:

35xy-5x-56y+8=(35xy-5x)-(56y-8)
=5x(7y-1)-8(7y-1)
=(5x-8)(7y-1).

May 10, 2015

First note that the first group of two terms have a common factor of 5x, so 35xy-5x-56y+8=5x(7y-1)-56y+8. Next, factor -8 out of the second group of two terms to get 5x(7y-1)-8(7y-1). Now both of these terms have a factor of (7y-1) that can be factored out. The final answer is 35xy-5x-56y+8=(7y-1)(5x-8).

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).

color(red)((35xy-5x)) - color(blue)((56y-8))

= color(red)((5x)(7y-1)) - color(blue)((8)(7y-1))

= (5x-8)(7y-1)