If a polynomial has four terms, you can sometimes factor it by grouping it, and factoring one part at a time. You may have to experiment to find the correct combination (and, of course, it is possible that this method doesn't work at all). In this case:
ab + 3a - 2b - 6
= (ab + 3a) - (2b + 6)
= a(b + 3) - 2(b + 3)
= (a - 2)(b + 3)
Note the common factor, (b + 3), in the third step. If you don't get this common factor, you can't continue, and may have to try other grouping combinations.
ab-2ac+b^2-2bc
You want: abc + ab Factor out the common terms which are "a" and "b" ab ( c + 1 )
(a + b)(b + c)
(a + 3)( b + 2)
x2y + axy + abx + a2b Factor by grouping. xy(x + a) + ab(x + a) (xy + ab)(x + a)
ab + 4 + a + 4b factors to (a + 4)(b + 1)
The GCF is a.
a(b+3)+b(b+3)
(a - c)(b - d)
(a + b)(b - 2c)
(a + b)(b - 2c)
(a+b)(a squared-ab+b squared)