To "expand" the squares of the parenthesized expressions,

**multiply them out** and then simplify the result. For instance:

. . . . .$\displaystyle (x\, +\, 3)^2\, +\, (y\, -\, 1)^2\, =\, 9$

. . . . .$\displaystyle (x\, +\, 3)(x\, +\, 3)\, +\, (y\, -\, 1)(y\, -\, 1)\, =\, 9$

. . . . .$\displaystyle x^2\, +\, 6x\, +\, 9\, +\, y^2\, -\, 2y\, +\, 1\, =\, 9$

. . . . .$\displaystyle x^2\, +\, y^2\, +\, 6x\, -\, 2y\, +\, 10\, =\, 9$

. . . . .$\displaystyle x^2\, +\, y^2\, +\, 6x\, -\, 2y\, +\, 1\, =\, 0$

:D