Factorise 9a^2+6ab.

So what does it mean when we factorise? Well, we want to take the highest common factor (HCF) of both of these algebraic terms and we want to take that outside the back to simplify the expression. First, let's look at the numbers in both terms - 9 and 6. What is the highest times table that has both of these numbers - 3 times tables. We can now take a 3 outside the bracket, 3(3a^2+2ab). You can now see that we have replaced the number in each terms with how many times it fits into the 3 times table. Now, let's turn our attention to our letters in the expression - what is common in both terms? 'a' is common in both terms but 'b' is not. Using the same method, we take 'a' outside the brackets. Let's look at our factorisation now - 3a(3a+2b). Double check that you have fully factorised. A good way to check that you have the correct answer is to expand what you have found to see whether you end at the expression you started with.
Final answer: 3a(3a+2b)