Question

(1/2m-1/3) (1/2m+1/3) (1/4m square+1/9)

Answer 1

(1/2m-1/3)(1/2m+1/3)(1/4m²+1/9)
= (1/4m²-1/9)(1/4m²+1/9)
= (1/16m^4 - 1/81)

Answer 2

(1/2m-1/3) (1/2m+1/3) (1/4m square+1/9)
here (1/2m-1/3) (1/2m+1/3) is in the form of (a+b)(a-b)
formulae for (a+b)(a-b) is a^2-b^2
by comparing here we have a=1/2m and b=-1/3
(1/2m-1/3) (1/2m+1/3) (1/4m square+1/9)
⇒(1/2m)^2-(1/3)^2 (1/4m square+1/9)=(1/4m^2-1/9) (1/4m^2+1/9)
again applying formulae for (a+b)(a-b) is a^2-b^2
we have
(1/4m^2-1/9) (1/4m^2+1/9)=(1/4m^2)^2-(1/9)^2
=1/16m^4-1/81