Solve 3xy*(2x-2y)-2y^2*(x+y)-2y*(3x^2-y^2)+16xy^2=

$$3 x y \cdot ( 2 x - 2 y ) - 2 y ^ { 2 } \cdot ( x + y ) - 2 y \cdot ( 3 x ^ { 2 } - y ^ { 2 } ) + 16 x y ^ { 2 } =$$

Evaluate

$$8xy^{2}$$

Solution Steps

Use the distributive property to multiply 3xy by 2x-2y.

$$6x^{2}y-6xy^{2}-2y^{2}\left(x+y\right)-2y\left(3x^{2}-y^{2}\right)+16xy^{2}$$

Use the distributive property to multiply -2y^{2} by x+y.

$$6x^{2}y-6xy^{2}-2y^{2}x-2y^{3}-2y\left(3x^{2}-y^{2}\right)+16xy^{2}$$

Combine -6xy^{2} and -2y^{2}x to get -8xy^{2}.

$$6x^{2}y-8xy^{2}-2y^{3}-2y\left(3x^{2}-y^{2}\right)+16xy^{2}$$

Use the distributive property to multiply -2y by 3x^{2}-y^{2}.

$$6x^{2}y-8xy^{2}-2y^{3}-6yx^{2}+2y^{3}+16xy^{2}$$

Combine 6x^{2}y and -6yx^{2} to get 0.

$$-8xy^{2}-2y^{3}+2y^{3}+16xy^{2}$$

Combine -2y^{3} and 2y^{3} to get 0.

$$-8xy^{2}+16xy^{2}$$

Combine -8xy^{2} and 16xy^{2} to get 8xy^{2}.

$$8xy^{2}$$

Expand

$$8xy^{2}$$

Solution Steps

Use the distributive property to multiply 3xy by 2x-2y.

$$6x^{2}y-6xy^{2}-2y^{2}\left(x+y\right)-2y\left(3x^{2}-y^{2}\right)+16xy^{2}$$

Use the distributive property to multiply -2y^{2} by x+y.

$$6x^{2}y-6xy^{2}-2y^{2}x-2y^{3}-2y\left(3x^{2}-y^{2}\right)+16xy^{2}$$

Combine -6xy^{2} and -2y^{2}x to get -8xy^{2}.

$$6x^{2}y-8xy^{2}-2y^{3}-2y\left(3x^{2}-y^{2}\right)+16xy^{2}$$

Use the distributive property to multiply -2y by 3x^{2}-y^{2}.

$$6x^{2}y-8xy^{2}-2y^{3}-6yx^{2}+2y^{3}+16xy^{2}$$

Combine 6x^{2}y and -6yx^{2} to get 0.

$$-8xy^{2}-2y^{3}+2y^{3}+16xy^{2}$$

Combine -2y^{3} and 2y^{3} to get 0.

$$-8xy^{2}+16xy^{2}$$

Combine -8xy^{2} and 16xy^{2} to get 8xy^{2}.

$$8xy^{2}$$