Question

Written in simplest form, the expression (x^2)(y^2)-9 over 3-xy is equivalent to

1. -1
2. 1 over 3+xy
3. -(3+xy)
4. 3+xy
Please show work

Answer 1

((x^2)(y^2) - 9) *(3 - xy).

Note difference of two squares: (a^2 - b^2) = (a-b)(a+b)
(x^2)(y^2) - 9 = (xy)^2 - 3 ^2 = (xy - 3)(xy + 3). (Take note)

(3- xy) = -(xy - 3). (Take note of this also)

Your question said: ((x^2)(y^2) - 9) times (3 - xy),
Don't you think it should be divide? Would solve it as divide.

((x^2)(y^2) - 9) /(3 - xy) = (xy - 3)(xy + 3) / -(xy - 3)

= -(xy + 3).

Answer is (3). Solved it as divide. Using times gives none of the solution among the options.
Cheers.