Solve {l}{(3x+y)(x-y)}{+2xy-y^2}

$$\left. \begin{array} { l } { ( 3 x + y ) ( x - y ) } \\ { + 2 x y - y ^ { 2 } } \end{array} \right.$$

Evaluate

$$3x^{2}-2y^{2}$$

Solution Steps

Use the distributive property to multiply 3x+y by x-y and combine like terms.

$$3x^{2}-2xy-y^{2}+2xy-y^{2}$$

Combine -2xy and 2xy to get 0.

$$3x^{2}-y^{2}-y^{2}$$

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

$$3x^{2}-2y^{2}$$

Expand

$$3x^{2}-2y^{2}$$

Solution Steps

Use the distributive property to multiply 3x+y by x-y and combine like terms.

$$3x^{2}-2xy-y^{2}+2xy-y^{2}$$

Combine -2xy and 2xy to get 0.

$$3x^{2}-y^{2}-y^{2}$$

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

$$3x^{2}-2y^{2}$$