What does multiply by the reciprical mean

It means multiply by the reciprocal of the number. The reciprocal is 1 divided by the number (x).

So assuming you're number is 3, the reciprocal of 3 would be 1/3. 

or 

Assuming the number is 0.2, the reciprocal of the number would be 1/0.2

(m+11n)^2=(m+11n)(m+11n)=m^2+11mn+11mn+121n^2=m^2+22mn×121n^2 for example; use foil: (a+b)(a+b)first. a^2outside. abinside. ablast. b^2