Factor: x^2 - 7x - 9x + 63 ?

Normally we'd just combine the -7x and -9x to simplify it, but with the way that this is written, there's another trick you can use:

x^2 - 7x - 9x + 63
x(x-7) - 9x + 63
x(x-7) - 9(x-7)

Both terms have (x-7) so you can factor this out too:
(x-9)(x-7)

Written that way, it's pretty clear, reversing the FOIL method:

(x - 7)(x - 9)

x ² - 16 x + 63
( x - 9 ) ( x - 7 )

x^2 - 7x - 9x + 63
= (x^2 - 7x) - (9x - 63)
= x(x - 7) - 9(x - 7)
= (x - 7)(x - 9)

x^2 - 7x - 9x + 63
You could try grouping
=(x^2 - 7x) - (9x - 63)
=x(x - 7) - 9(x - 7)
= (x - 7)(x - 9)

Or you could combine similar terms and factor as a quadratic trinomial.
x^2 - 16x + 63
=(x - 7)(x - 9)

x^2-7x-9x+63

Separate the two:
(x^2-7x) AND (-9x+63)

And factor the two:
(x^2-7x) = x(x-7)

(-9x+63) = -9(x-7)

Just to be sure, the second factors should be the same, just to prove that you did it right.

Combine the two to find answer:
(x-9)(x-7)

First, combine likes terms
so, x^2 - 16x + 63
now, factor
(x-7)(x-9)
Those are the numbers you originally had, but it could have been
x^2 - 7x - 9x - 80 which is NOT factored as (x-7)(x-9) but as (x-20)(x+4)

combine like terms
x^2 - 16x + 63
(x - 9)(x - 7)

x^2 - 7x - 9x + 63
x^2 - 16x + 63
(x - 7)(x - 9)