Is "first member" or "second member" proper mathematical English to refer to the LHS or RHS of an equation? Is "first member" or "second member" proper modern mathematical English to refer to the left-hand side (LHS) or right-hand side (RHS) of an equation, respectively?
 A: Better standards are to write
\begin{align}(x-1)^2&=(x-1)(x-1)\tag1 \\&=x^2-x-x+1\tag2\\&=x^2-2x+1\tag3\end{align}
and then refer to the left-hand side (LHS) of $(1)$ or the right-hand side (RHS) of $(3)$.

Regarding the edited question, Google does give some results for "member of the equation". Then again they may be very old, or written by non-native speakers. I've personally never heard it.
A: James & James's 1992 Mathematics Dictionary p. 270 gives:

MEM'BER, n. member of an equation. The expression on one (or the other) side of the equality sign. The two members of an equation are distinguished as the left or first and the right or second member.

OED's definition for "member":

7. b. Either of the two sides of an equation.

The quotes it gives for this usage:

1702   J. Raphson Math. Dict.   "Equation, (in Algebra) is a Comparison between two Quantities (or Members of the Equation,) to make them equal."
a1831   Encycl. Metrop. (1845) I. 544/2   "Both members of an equation may be raised to the same power, or the same root of them may be extracted."
1859   Ladies' Repository Oct. 626/1   "The equation to be solved is, $x^4−2x^3+x=132$, which, by $\color{green}{\mathrm{transposing*}}$ the second member, may be put under the form, $x^4−2x^3+x-132$."
1903   J. Walker Introd. Physical Chem. (ed. 3) xxvi. 307:   "Eliminating what is common to both members of the equation."
1972   M. Kline Math. Thought v. 122:   "An expression corresponding to the left or right member reappears under the concept of anharmonic ratio in the work of Pappus and in later work on projective geometry."

So it does appear this is proper (albeit probably rare) modern mathematical English.
$\color{green}{\mathrm{*}}$James & James p. 426:TRANS-POSE, n., v. To move a term from onemember of an equation to the other and changeits sign. This is equivalent to subtracting the termfrom both members. The equation $x + 2 = 0$ yields $x = - 2$ after transposing the $2$.OED's "transpose" 5. b.:Algebra. To transfer (a quantity) from one side of an equation to the other, with change of sign.
