How to write the sum of numbers as the product of their gcf and another sum
44+40?

Well, if that's the question, then you'll probably need to know
what their GCF is. Does that sound reasonable to you ?

What's the GCF of  44  and  40  ?

The factors of  44  are:  1,  2,  4,  11, and  44 .

The factors of  40  are:  1,  2,  4,  5,  8,  10,  20, and  40 .

The common factors are:  1,  2,  and  4 .

The greatest one is  4 .  <== GCF 

OK.

Now, what's each number as a product of the GCF and something else "

         44  is  4  times  11

         40  is  4  times  10.

So . . . . . (44 + 40)  is the same thing as   4 times (11 + 10) .