(2x+5y)(3x^2-4xy+2y^2)

First, multiply the first term in the first parenthesis by every term in the polynomial.

\((2x)(3x^2)+(2x)(-4xy)+(2x)(2y^2)+(5y)(3x^2-4xy+2y^2)\)

Simplify.

\((2x)(3x^2)=6x^3, (2x)(-4xy)=-8x^2y, (2x)(2y^2)=4xy^2\)

\(6x^3-8x^2y+4xy^2+(5y)(3x^2-4xy+2y^2)\)

Now distribute the 5y.

\(6x^3-8x^2y+4xy^2+(5y)(3x^2)+(5y)(-4xy)+(5y)(2y^2)\)

Simplify.

\((5y)(3x^2)=15x^2y, (5y)(-4xy)=-20xy^2, (5y)(2y^2)=10y^3\)

\(6x^3-8x^2y+4xy^2+15x^2y-20xy^2+10y^3\)

Reorganize.

\(6x^3-8x^2y+15x^2y+4xy^2-20xy^2+10y^3\)

Combine like terms.

\(-8x^2y+15x^2y=7x^2y, 4xy^2-20xy^2=-16xy^2\)

\(6x^3+7x^2y-16xy^2+10y^3\)

This is the same as Guest's answer but LaTeX makes it easier to read.