When factoring 9s + 12, we need to see if there is a common factor between our numbers that we can factor out of our expression. In this math question, both 9 and 12 have a factor of 3. Therefore, we can take the factor 3 and place it on the outside of our expression, so it looks like this: 3(_s + _). We then think of what we would need to multiply by 3 in order to get our original numbers. Since 3x3 = 9, and 3x4 = 12, we can complete our factorization as follows 3(3s + 4).
If we were to distribute to check our work, we would multiply what is on the outside by what is on the inside. First, 3x3s = 9s, and 3x4 = 12, with an addition sign in between. That is 9s + 12, which is our original expression, so we know we have solved the question correctly.