a)\(\left(-a+\frac{2}{3}\right)\left(a+\frac{2}{3}\right)=\left(\frac{2}{3}-a\right)\left(\frac{2}{3}+a\right)=\left(\frac{2}{3}\right)^2-a^2=\frac{4}{9}-a^2\)
b)\(\left(x+5\right)\left(x^2-5x+25\right)=x^3+5^3=x^3+125\)
c)\(\left(1-x\right)\left(x^2+x+1\right)=1-x^3\)
d)\(\left(a^2-2a+3\right)\left(a^2+2a+3\right)=\left(a^2+3\right)^2-\left(2a\right)^2=\left(a^2+3\right)^2-4a^2\)
e)\(\left(x+3y\right)\left(9y^2-3xy+x^2\right)=x^3+\left(3y\right)^3=x^3+9y^3\)
f)\(2\left(x-\frac{1}{2}\right)\left(4x^2+2x+1\right)=\left(2x-1\right)\left(4x^2+2x+1\right)=\left(2x\right)^3-1=8x^3-1\)