Trinomials

[temarie]

find the value of c which will make the following expression a perfect square trinomial
9x^2-24x+c

I can factor trinomials but having trouble reversing to get c

 

[BigGlenntheHeavy]

\(\displaystyle (a-b)^2 \ = \ a^2-2ab+b^2\)

\(\displaystyle 9x^2-24x+c, \ \implies \ a^2 \ = \ 9x^2 \ \implies \ a \ = \ 3x.\)

\(\displaystyle -24x \ = \ -2ab, \ 12x \ = \ ab \ = \ 3xb, \ b \ = \ 4, \ c \ =b^2, \ c \ =16\)

\(\displaystyle Check3x-4)^2 \ = \ 9x^2 \ -24x \ +16.\)