How do you factor completely #2bx+2x-2by-2y#?
There is a common factor of 2 in all 4 terms which can be taken out.
hence 2 (bx + x - by -y).............(A)
now take out the common factor of x in the first 2 terms inside bracket.
thus bx + x = x(b +1)
Similarly a common factor of -y can be removed from the 2 remaining terms.
thus -by - y = -y(b + 1)
now bx+x-by-y = x(b+1)-y(b + 1)
There is a common factor of (b +1) here.
hence: (b +1)(x -y) when factorised.
Putting this back into (A) gives.
2bx+2x-2by-2y = 2(b+1)(x-y)
Same answer, just a different presentation
Sometimes these are spotted straight away, other times not and need a bit of work.
Looking for common factors within each bracket
Notice that 2 is a common factor in the last bracket