Solve 9x(x-y)-y(x-2)-x(x+2x)-6x^2-2(1+x)+y(x-2)+2

$$9 x ( x - y ) - y ( x - 2 ) - x ( x + 2 x ) - 6 x ^ { 2 } - 2 ( 1 + x ) + y ( x - 2 ) + 2$$

Evaluate

$$-9xy-2x$$

Solution Steps

Use the distributive property to multiply 9x by x-y.

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

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

$$9x^{2}-9xy-\left(yx-2y\right)-x\left(x+2x\right)-6x^{2}-2\left(1+x\right)+y\left(x-2\right)+2$$

To find the opposite of yx-2y, find the opposite of each term.

$$9x^{2}-9xy-yx+2y-x\left(x+2x\right)-6x^{2}-2\left(1+x\right)+y\left(x-2\right)+2$$

Combine -9xy and -yx to get -10xy.

$$9x^{2}-10xy+2y-x\left(x+2x\right)-6x^{2}-2\left(1+x\right)+y\left(x-2\right)+2$$

Combine x and 2x to get 3x.

$$9x^{2}-10xy+2y-x\times 3x-6x^{2}-2\left(1+x\right)+y\left(x-2\right)+2$$

Multiply x and x to get x^{2}.

$$9x^{2}-10xy+2y-x^{2}\times 3-6x^{2}-2\left(1+x\right)+y\left(x-2\right)+2$$

Combine 9x^{2} and -x^{2}\times 3 to get 6x^{2}.

$$6x^{2}-10xy+2y-6x^{2}-2\left(1+x\right)+y\left(x-2\right)+2$$

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

$$-10xy+2y-2\left(1+x\right)+y\left(x-2\right)+2$$

Use the distributive property to multiply -2 by 1+x.

$$-10xy+2y-2-2x+y\left(x-2\right)+2$$

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

$$-10xy+2y-2-2x+yx-2y+2$$

Combine -10xy and yx to get -9xy.

$$-9xy+2y-2-2x-2y+2$$

Combine 2y and -2y to get 0.

$$-9xy-2-2x+2$$

Add -2 and 2 to get 0.

$$-9xy-2x$$

Expand

$$-9xy-2x$$

Solution Steps

Use the distributive property to multiply 9x by x-y.

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

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

$$9x^{2}-9xy-\left(yx-2y\right)-x\left(x+2x\right)-6x^{2}-2\left(1+x\right)+y\left(x-2\right)+2$$

To find the opposite of yx-2y, find the opposite of each term.

$$9x^{2}-9xy-yx+2y-x\left(x+2x\right)-6x^{2}-2\left(1+x\right)+y\left(x-2\right)+2$$

Combine -9xy and -yx to get -10xy.

$$9x^{2}-10xy+2y-x\left(x+2x\right)-6x^{2}-2\left(1+x\right)+y\left(x-2\right)+2$$

Combine x and 2x to get 3x.

$$9x^{2}-10xy+2y-x\times 3x-6x^{2}-2\left(1+x\right)+y\left(x-2\right)+2$$

Multiply x and x to get x^{2}.

$$9x^{2}-10xy+2y-x^{2}\times 3-6x^{2}-2\left(1+x\right)+y\left(x-2\right)+2$$

Combine 9x^{2} and -x^{2}\times 3 to get 6x^{2}.

$$6x^{2}-10xy+2y-6x^{2}-2\left(1+x\right)+y\left(x-2\right)+2$$

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

$$-10xy+2y-2\left(1+x\right)+y\left(x-2\right)+2$$

Use the distributive property to multiply -2 by 1+x.

$$-10xy+2y-2-2x+y\left(x-2\right)+2$$

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

$$-10xy+2y-2-2x+yx-2y+2$$

Combine -10xy and yx to get -9xy.

$$-9xy+2y-2-2x-2y+2$$

Combine 2y and -2y to get 0.

$$-9xy-2-2x+2$$

Add -2 and 2 to get 0.

$$-9xy-2x$$