(2x + 3y)^2 – (2x – 3y)^2 = 360 show that xy is a multiple of 5

Expand first brackets:

4x2+6xy+6xy+9y2

Expand second brackets:

4xy2-6xy-6xy+9y2

Subtract the second expansion from the first one, being careful of the double negative:

=24xy

Then, back into the original equation:

24xy=360

Divide both sides by 24:

xy=15

Divide by 5:

(xy)/5=3

The result is an integer, so xy is a multiple of 5

Answered by Ryan M. Maths tutor

9007 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

The first floor of an ancient japanese tower has 150 steps. Each floor above has 5 fewer floors than the previous. So, the second floor has 145 steps, the third 140 etc. How many floors does the tower have if the final floor has 30 steps leading to it.


How would you work out the length of an hypotenuse, if the length of the opposite side is 3 cm and the length of the opposite side is 4 cm?


Find the solutions of the equation x^2 - 2x - 8 =0


How can I solve simultaneous equations?


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences