There are so many questions like this that perhaps it would be easier to describe the method of solution and let the user work out the answer for himself/herself. I'll use this question as an example.
The question contains two terms added together. But they have factors in common. The idea is to find the largest common factor by inspecting the two terms and looking for everything they have in common. A term is made up of plain numbers and variables. In this case, the variables, v and w, are raised to certain powers, but as long as we're dealing with the same variables we can combine powers (exponents).
Look at the numbers first. We have 9 and 33 only, because the others are exponents. What's the gcf of these? Break them down into factors: 9=3*3; 33=3*11, so gcf=3, because it's the only common factor in this case. Note this. Now take the v terms: what's the lowest exponent? v^4. Note that; now we have 3v^4 so far as the gcf. Now w: the lowest exponent is w^3. We have the gcf: 3v^4w^3. When we factorise the expression we get: 3v^4w^3(3v^2+11w^2). expand the brackets: 3*3 * v^4*v^2 * w^3 + 3*11 * v^4 * w^3*w^2 = 9v^6w^3+33v^4w^5, the original expression. When we multiply the same variables with exponents we add the exponents together to get the product.
Now try answering your own gcf questions! It should be easy!
