Expand and simplify (x-3)(3x+5)

This question requires us to know how to multiply out the brackets and collect like terms together. It is worth 3 marks in total. First, we draw a smiley face on the brackets in the question: link the x and 3x to get the left eye, link the -3 and the 5 to get the right eye, link the x and the 5 to get the mouth and link the -3 and the 3x to get the nose. Each of these are the pairs we need to multiply together to get our 4 terms. The first term is x multiplied by 3x and we get 3x^2. The second term is -3 multiplied by 5 and we get -15. The third term is x multiplied by 5 and we get 5x. The fourth term is -3 multiplied by 3x and we get -9x. We add the four terms together and we get that (x-3)(3x+5) = 3x^2-15+5x-9x. This would give us the first mark. Now, we need to collect like terms, these are the terms which have x to the same power. Here, we collect 5x-9x = -4x. This would give us the second mark. We also need to order the terms so that the powers of x are decreasing from x^2 to x to having no x at all. So, the final answer is 3x^2-4x-15. This would give us the third mark. Well done!