Expanding a Quadratic equation?

Question

I cannot remember - when expanding a quadratic with variables only
eg - (st-tr)^2

do you square both of the variables or the "set"?

Would the answer look like?
A) (st^2 - 2st^2r + tr^2)
or
B) (s^2 t^2 - 2st^2r + t^2 r^2)

this isnt the whole question just a step in the question & I am forgetting my basic quad solving ....

Thanks

Answer 1

expanding

s'2 t'2 - 2st'2r + t'2 r'2

answer is b)

Answer 2

Neither of the answers A and B given by you are correct for the quadratic you have mentioned. You have to square all items in the first term and second term.
The answer to (st-tr)^2 would be
(st)^2-2*(st)(tr)+(tr)^2 =
s^2*t^2-2*s*r*t^2+t^2*r^2=
t^2*(s^2-2*s*r+r^2) since t^2 is common to all terms. (t could alsohave been separated before the expansion was done.)

Answer 3

let st =a and tr =b so you have (a-b)^2 which we know is = a^2 -2ab +b^2,
then substitute; (st)^2 -2(st)(tr) + (tr)^2 now expand
(s^2)(t^2) - 2(sr(t^2)) + (t^2)(r^2), factor out (t^2) to get:

(st-tr)^2 = (t^2)*[(s^2) - 2(sr) + (r^2)]

Answer 4

Well if you follow standard FOIL-ing, then you would get B as it is a^2 + 2ab + b^2. So for (st)^2, you would have to distribute the exponent.

Answer 5

i think you would have to find the square root of everything in the parenthesis.. it would be..
(st-tr)(st-tr)
then u just factor that..or do whatever it is ur gonna do with it.idk.

Answer 6

(st-tr)^2 = (st) x (st) - 2 x (st) (tr) + (tr ) x(tr)

= (s^2) (t^2) - 2 x {s (t^2 ) r }+ (t^2 ) (r^2).