Start with the product of two binomials (with four different variables), expand it, and simplify it. The final result will be the required four-term polynomial.
Let's consider the following four-term polynomial.
12px + 8py - 3qx - 2qy
As we can see, the first two terms have p in common and the last two terms have q in common. We should group them together.
(12px + 8py) + (-3qx + 2qy)
By writing 12 as 4* 3 and 8 as 4* 2, we can rewrite our polynomial above as follows.
( 4* 3 px + 4* 2 py) + ( -3 qx - 2 qy)
Next, we can factor out 4p from the first two terms and - q from the last two terms.
4p( 3x + 2y) - q( 3x + 2y)
Notice that ( 3x+2y) is common in both groups and we can factor it out.
( 4p - q)( 3x + 2y)
As we can see, we have factored the initial polynomial by grouping. Keep in mind that the polynomial used here is just a sample and your answer may vary.
Extra
How to Find the Polynomial?
One way of finding the required polynomial is to start with the product of two binomials with four different variables.
(4p - q)(3x + 2y)
Second, we expand the product above and simplify it.
