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

3 Answers
George C.
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)#.

Bill K.
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)#.

Alan P.
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)#

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