What rule do I break here?

[Jherek2]

I'm factoring the difference of two cubes: mx³+my³-x-y,
I get this far
m(x+y)(x²+xy+y²)-x-y
and then I do this
m(x+y)(x²+xy+y²)-1(x+y) to get (m-1)(x+y)(x²+xy+y²) which is wrong.

I've worked out what I should have done (I think!),
(x+y)m(x²+xy+y²)-x-y
(x+y)(mx²+mxy+my²)-x-y
(x+y)(mx²+mxy+my²)-1(x+y)
(x+y)(mx²+mxy+my²-1)

The worrying thing is, I don't know WHY I can't do what I did when I went wrong ! So how do I recognise when I'm going to do it again?

[stapel_eliz]

I'm factoring the difference of two cubes: mx³+my³-x-y,
I get this far
m(x+y)(x²+xy+y²)-x-y
and then I do this
m(x+y)(x²+xy+y²)-1(x+y) to get (m-1)(x+y)(x²+xy+y²) which is wrong....

The worrying thing is, I don't know WHY I can't do what I did when I went wrong

Try highlighting things in excruciating clarity...

. . . . .m(x + y)(x² + xy + y²) - x - y

. . . . .m(x + y)(x² + xy + y²) - 1(x + y)

Can you see now that the only thing that factors out front is the (x + y), leaving the m(x² + xy + y²) - 1 to be combined and simplified inside the parentheses?

[Jherek2]

Thank you for the explanation . When someone shows me something I'm stuck on, it always seems so easy! I need to slow down a bit and get more practice!