a: \(\left(2x+1\right)\left(4y-3\right)-8x\left(y+2\right)\)
\(=8xy-6x+4y-3-8xy-16x\)
=-22x+4y-3
b: \(\left(x-5\right)\left(2y+1\right)+\left(2x+1\right)\left(y-5\right)\)
\(=2xy+x-10y-5+2xy-10x+y-5\)
=4xy-9x-9y-10
c: \(\left(2x+y\right)\left(4x^2-2xy+y^2\right)\)
\(=8x^3-4x^2y+2xy^2+4x^2y-2xy^2+y^3\)
\(=8x^3+y^3\)
d: \(\left(\dfrac{1}{3}x+\dfrac{2}{5}y\right)\left(\dfrac{1}{3}x-\dfrac{2}{5}y\right)\)
\(=\dfrac{1}{9}x^2-\dfrac{2}{15}xy+\dfrac{2}{15}xy-\dfrac{4}{25}y^2\)
\(=\dfrac{1}{9}x^2-\dfrac{4}{25}y^2\)
e: \(\left(x+y\right)\left(x^2+2xy+y^2\right)\)
\(=x^3+2x^2y+xy^2+x^2y+2xy^2+y^3\)
\(=x^3+3x^2y+3xy^2+y^3\)