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!

Answered by Martha P. Maths tutor

4042 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

How do I add two fractions? (plus example)


Evaluate x^2 +2x -4 = 0


A rectangular path has perimeter of 240m. If the rectangle is split lengthways, two paths of 160m are formed. Work out the lengths of the sides of the original path.


Solve 2x + 4 > 16


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo
Cookie Preferences