Question

Factor completely: 4ab − 7ax + 8b − 14x

Answer 1

Notice how some of the coefficients have factors in common - like 4 and 8, 7 an 14? Well, that's the trick. You have to use the general principle that AC + BC = (A + B) C (i.e. the distributive law).

Let's try moving things around, maybe that'll make it clearer:

(4ab + 8b) + (-7ax - 14x)

Then you factor out 4a and -7x from the respective parts, which gives you 4b(a + 2) - 7x(a + 2), right?
But that is just (4b - 7x)(a + 2)
(You can check it by multiplying the factors.)

The other one is similar: 9xy + 36x = 9x (y + 4), and -10y - 40 = -10 (y + 4)
so the whole thing is 9x (y + 4) -10 (y + 4) = (9x -10) (y + 4).

At first these things look tough to factor but once you see that there's a trick to it, it should be easy. I hope this has helped.

Answer 2

group in pairs

4ab +8b -7ax -14x

4b(a + 2) -7x(a + 2)

(a + 2) is a common factor

(a+2)(4b - 7x)