Completely factor the following expression.1.)

Question

5c^2-24cd-5d^2

Answer 1

(5c+d)(c-5d)
It's got to be something of the form (ac+bd)(ec-fd) for some a, b, e and f, but 5 is a prime number, so a and e must be 5 and 1 (or the other way around), and likewise b and f. Also, the -24 can be got as -5x5 + 1, so you just need to experiment a little with the four coefficients until you get the right combination.