Multiply $ \color{blue}{2} $ by $ \left( x+y\right) $ $$ \color{blue}{2} \cdot \left( x+y\right) = 2x+2y $$

Multiply each term of $ \left( \color{blue}{2x+2y}\right) $ by each term in $ \left( x+y+1\right) $.

$$ \left( \color{blue}{2x+2y}\right) \cdot \left( x+y+1\right) = 2x^2+2xy+2x+2xy+2y^2+2y $$

Combine like terms:

$$ 2x^2+ \color{blue}{2xy} +2x+ \color{blue}{2xy} +2y^2+2y = 2x^2+ \color{blue}{4xy} +2y^2+2x+2y $$

Multiply each term of $ \left( \color{blue}{2x^2+4xy+2y^2+2x+2y}\right) $ by each term in $ \left( x+y-1\right) $.

$$ \left( \color{blue}{2x^2+4xy+2y^2+2x+2y}\right) \cdot \left( x+y-1\right) = \\ = 2x^3+2x^2y -\cancel{2x^2}+4x^2y+4xy^2-4xy+2xy^2+2y^3 -\cancel{2y^2}+ \cancel{2x^2}+2xy-2x+2xy+ \cancel{2y^2}-2y $$

Combine like terms:

$$ 2x^3+ \color{blue}{2x^2y} \, \color{red}{ -\cancel{2x^2}} \,+ \color{blue}{4x^2y} + \color{orange}{4xy^2} \color{blue}{-4xy} + \color{orange}{2xy^2} +2y^3 \, \color{red}{ -\cancel{2y^2}} \,+ \, \color{red}{ \cancel{2x^2}} \,+ \color{orange}{2xy} -2x+ \color{orange}{2xy} + \, \color{red}{ \cancel{2y^2}} \,-2y = 2x^3+ \color{blue}{6x^2y} + \color{orange}{6xy^2} +2y^3-2x-2y $$