Solve (3x-2y+1)^2+(2x-y+2)(-2+y-2x)-x(5x-8y)

$$( 3 x - 2 y + 1 ) ^ { 2 } + ( 2 x - y + 2 ) ( - 2 + y - 2 x ) - x ( 5 x - 8 y )$$

Evaluate

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

Solution Steps

Square 3x-2y+1.

$$9x^{2}-12xy+6x+4y^{2}-4y+1+\left(2x-y+2\right)\left(-2+y-2x\right)-x\left(5x-8y\right)$$

Use the distributive property to multiply 2x-y+2 by -2+y-2x and combine like terms.

$$9x^{2}-12xy+6x+4y^{2}-4y+1-8x+4xy-4x^{2}+4y-y^{2}-4-x\left(5x-8y\right)$$

Combine 6x and -8x to get -2x.

$$9x^{2}-12xy-2x+4y^{2}-4y+1+4xy-4x^{2}+4y-y^{2}-4-x\left(5x-8y\right)$$

Combine -12xy and 4xy to get -8xy.

$$9x^{2}-8xy-2x+4y^{2}-4y+1-4x^{2}+4y-y^{2}-4-x\left(5x-8y\right)$$

Combine 9x^{2} and -4x^{2} to get 5x^{2}.

$$5x^{2}-8xy-2x+4y^{2}-4y+1+4y-y^{2}-4-x\left(5x-8y\right)$$

Combine -4y and 4y to get 0.

$$5x^{2}-8xy-2x+4y^{2}+1-y^{2}-4-x\left(5x-8y\right)$$

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

$$5x^{2}-8xy-2x+3y^{2}+1-4-x\left(5x-8y\right)$$

Subtract 4 from 1 to get -3.

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

Use the distributive property to multiply x by 5x-8y.

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

To find the opposite of 5x^{2}-8xy, find the opposite of each term.

$$5x^{2}-8xy-2x+3y^{2}-3-5x^{2}+8xy$$

Combine 5x^{2} and -5x^{2} to get 0.

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

Combine -8xy and 8xy to get 0.

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

Expand

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

Solution Steps

Square 3x-2y+1.

$$9x^{2}-12xy+6x+4y^{2}-4y+1+\left(2x-y+2\right)\left(-2+y-2x\right)-x\left(5x-8y\right)$$

Use the distributive property to multiply 2x-y+2 by -2+y-2x and combine like terms.

$$9x^{2}-12xy+6x+4y^{2}-4y+1-8x+4xy-4x^{2}+4y-y^{2}-4-x\left(5x-8y\right)$$

Combine 6x and -8x to get -2x.

$$9x^{2}-12xy-2x+4y^{2}-4y+1+4xy-4x^{2}+4y-y^{2}-4-x\left(5x-8y\right)$$

Combine -12xy and 4xy to get -8xy.

$$9x^{2}-8xy-2x+4y^{2}-4y+1-4x^{2}+4y-y^{2}-4-x\left(5x-8y\right)$$

Combine 9x^{2} and -4x^{2} to get 5x^{2}.

$$5x^{2}-8xy-2x+4y^{2}-4y+1+4y-y^{2}-4-x\left(5x-8y\right)$$

Combine -4y and 4y to get 0.

$$5x^{2}-8xy-2x+4y^{2}+1-y^{2}-4-x\left(5x-8y\right)$$

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

$$5x^{2}-8xy-2x+3y^{2}+1-4-x\left(5x-8y\right)$$

Subtract 4 from 1 to get -3.

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

Use the distributive property to multiply x by 5x-8y.

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

To find the opposite of 5x^{2}-8xy, find the opposite of each term.

$$5x^{2}-8xy-2x+3y^{2}-3-5x^{2}+8xy$$

Combine 5x^{2} and -5x^{2} to get 0.

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

Combine -8xy and 8xy to get 0.

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