Question

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

Answer 1

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)`.

Answer 2

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)`.

Answer 3

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)`