a, $[(a+b)-c]^{2}$=$(a+b)^{2}$-$2(a+b)c$-$c^{2}$ =$(a+b)^{2}$-$2(a+b)c$-$c^{2}$ =$a^{2}$ +$2ab$ +$b^{2}$ -$2ac$-$2bc $ -$c^2$
b, (5a-3b)$(5a+3b)$ =$25a^2$-$9b^2$
c, $(3x+1)(3x-1)$ = $9x^2$-$1$
d)$(5x^2-2)(5x^2+2)$ = $25x^4$-4
e) $(x^2+\frac{2y}{5})(x^2-\frac{2y}{5}))$ = $x^4$ -$\frac{4y^2}{25}$
f) $(x+y+z)(x+y-z)$ =$[(x+y)+z][(x+y)-z]$=$(x+y)^2)$-$z^2$ =$x^2+2xy+y^2$-$z^2$