Question

Factorise the following, using the identity a² - b² = (a - b)(a + b) : 36(p+q)²-64(p-q)²​

Answer 1

36(p+q)²-64(p-q)²​

Let p+q be a and p-q be b

36a^2-64b^2

=(6a)^2-(8b)^2

=(6a-8b)(6a+8b)

=2(3a-4b)(3a+4b)

=2(3p+3q-4p+4q)(3p+3q+4p-4q)

=2(7q-p)(7p-q)