Solve 2x(3x-2y)-3y(4x+y)-2(x^2-2y^2)

$$2 x ( 3 x - 2 y ) - 3 y ( 4 x + y ) - 2 ( x ^ { 2 } - 2 y ^ { 2 } )$$

Evaluate

$$4x^{2}-16xy+y^{2}$$

Solution Steps

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

$$6x^{2}-4xy-3y\left(4x+y\right)-2\left(x^{2}-2y^{2}\right)$$

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

$$6x^{2}-4xy-3y\left(4x+y\right)-2x^{2}+4y^{2}$$

Use the distributive property to multiply -3y by 4x+y.

$$6x^{2}-4xy-12yx-3y^{2}-2x^{2}+4y^{2}$$

Combine -4xy and -12yx to get -16xy.

$$6x^{2}-16xy-3y^{2}-2x^{2}+4y^{2}$$

Combine 6x^{2} and -2x^{2} to get 4x^{2}.

$$4x^{2}-16xy-3y^{2}+4y^{2}$$

Combine -3y^{2} and 4y^{2} to get y^{2}.

$$4x^{2}-16xy+y^{2}$$

Expand

$$4x^{2}-16xy+y^{2}$$

Solution Steps

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

$$6x^{2}-4xy-3y\left(4x+y\right)-2\left(x^{2}-2y^{2}\right)$$

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

$$6x^{2}-4xy-3y\left(4x+y\right)-2x^{2}+4y^{2}$$

Use the distributive property to multiply -3y by 4x+y.

$$6x^{2}-4xy-12yx-3y^{2}-2x^{2}+4y^{2}$$

Combine -4xy and -12yx to get -16xy.

$$6x^{2}-16xy-3y^{2}-2x^{2}+4y^{2}$$

Combine 6x^{2} and -2x^{2} to get 4x^{2}.

$$4x^{2}-16xy-3y^{2}+4y^{2}$$

Combine -3y^{2} and 4y^{2} to get y^{2}.

$$4x^{2}-16xy+y^{2}$$