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

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

Evaluate

$$-24x^{2}+12xy-15y^{2}$$

Solution Steps

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

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

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

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

Combine 2xy and 2xy to get 4xy.

$$3\left(-8x^{2}+4xy-3y^{2}-2y^{2}\right)$$

Combine -3y^{2} and -2y^{2} to get -5y^{2}.

$$3\left(-8x^{2}+4xy-5y^{2}\right)$$

Use the distributive property to multiply 3 by -8x^{2}+4xy-5y^{2}.

$$-24x^{2}+12xy-15y^{2}$$

Expand

$$-24x^{2}+12xy-15y^{2}$$

Solution Steps

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

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

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

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

Combine 2xy and 2xy to get 4xy.

$$3\left(-8x^{2}+4xy-3y^{2}-2y^{2}\right)$$

Combine -3y^{2} and -2y^{2} to get -5y^{2}.

$$3\left(-8x^{2}+4xy-5y^{2}\right)$$

Use the distributive property to multiply 3 by -8x^{2}+4xy-5y^{2}.

$$-24x^{2}+12xy-15y^{2}$$