What expression is equivalent to 10a + 6? Would it be 5(5a + 1)?

That wouldn't quite work, because if you were to multiply 5(5a + 1) out, you would end up with 25a +5, when you would want that to be 10a +6.

So you have to think of two numbers that would divide out of 10 and 6 equally. 6 and 3 wouldn't work, but 2 would.

We place a 2 on the outside then, and divide two from the two numbers.

10a + 6

2(5a + 3)

10a + 6  take out the greatest common factor = 2

So we have

2(5a + 3)        

Notice that   5(5a + 1) = 25a + 5.....  and that  couldn't possibly give us 10a + 6.....