a. $\left(\dfrac12 x+4\right)^2$
$= \left(\dfrac12 x\right)^2+2.\dfrac12 x.4 + 4^2$
$= \dfrac14x^2+4x+16$
b. $(7x-5y)^2$
$= (7x)^2-2.7x.5y+(5y)^2$
$= 49x^2-70xy+25y^2$
c. $(6x^2+y^2)^2(y^2-6x^2)$
$= (6x^2+y^2)(y^2+6x^2)(y^2-6x^2)$
$= (6x^2+y^2)[(y^2)^2-(6x^2)^2]$
$= (6x^2+y^2)(y^4-36x^4)$
$= 6x^2y^4-216x^6+y^6-36x^4y^2$
d. $(x+2y)^2$
$= x^2+2.x.2y+(2y)^2$
$= x^2+4xy+4y^2$
e. $(x-3y)(x+3y)$
$= x^2-(3y)^2$
$= x^2-9y^2$
f. $(5-x)^2$
$= 5^2-2.5.x+x^2$
$= 25-10x+x^2$