Solve 8x^{2}-{3x^2-6y-2x-3y-[9x^2-6y-4x]-(2x^2-9y+6x)-3x^2}

$$8 x ^ { 2 } - \{ 3 x ^ { 2 } - 6 y - 2 x - 3 y - [ 9 x ^ { 2 } - 6 y - 4 x ] - ( 2 x ^ { 2 } - 9 y + 6 x ) - 3 x ^ { 2 } \}$$

Evaluate

$$19x^{2}+4x-6y$$

Solution Steps

Combine -6y and -3y to get -9y.

$$8x^{2}-\left(3x^{2}-9y-2x-\left(9x^{2}-6y-4x\right)-\left(2x^{2}-9y+6x\right)-3x^{2}\right)$$

To find the opposite of 9x^{2}-6y-4x, find the opposite of each term.

$$8x^{2}-\left(3x^{2}-9y-2x-9x^{2}+6y+4x-\left(2x^{2}-9y+6x\right)-3x^{2}\right)$$

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

$$8x^{2}-\left(-6x^{2}-9y-2x+6y+4x-\left(2x^{2}-9y+6x\right)-3x^{2}\right)$$

Combine -9y and 6y to get -3y.

$$8x^{2}-\left(-6x^{2}-3y-2x+4x-\left(2x^{2}-9y+6x\right)-3x^{2}\right)$$

Combine -2x and 4x to get 2x.

$$8x^{2}-\left(-6x^{2}-3y+2x-\left(2x^{2}-9y+6x\right)-3x^{2}\right)$$

To find the opposite of 2x^{2}-9y+6x, find the opposite of each term.

$$8x^{2}-\left(-6x^{2}-3y+2x-2x^{2}+9y-6x-3x^{2}\right)$$

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

$$8x^{2}-\left(-8x^{2}-3y+2x+9y-6x-3x^{2}\right)$$

Combine -3y and 9y to get 6y.

$$8x^{2}-\left(-8x^{2}+6y+2x-6x-3x^{2}\right)$$

Combine 2x and -6x to get -4x.

$$8x^{2}-\left(-8x^{2}+6y-4x-3x^{2}\right)$$

Combine -8x^{2} and -3x^{2} to get -11x^{2}.

$$8x^{2}-\left(-11x^{2}+6y-4x\right)$$

To find the opposite of -11x^{2}+6y-4x, find the opposite of each term.

$$8x^{2}+11x^{2}-6y+4x$$

Combine 8x^{2} and 11x^{2} to get 19x^{2}.

$$19x^{2}-6y+4x$$

Expand

$$19x^{2}+4x-6y$$

Solution Steps

Combine -6y and -3y to get -9y.

$$8x^{2}-\left(3x^{2}-9y-2x-\left(9x^{2}-6y-4x\right)-\left(2x^{2}-9y+6x\right)-3x^{2}\right)$$

To find the opposite of 9x^{2}-6y-4x, find the opposite of each term.

$$8x^{2}-\left(3x^{2}-9y-2x-9x^{2}+6y+4x-\left(2x^{2}-9y+6x\right)-3x^{2}\right)$$

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

$$8x^{2}-\left(-6x^{2}-9y-2x+6y+4x-\left(2x^{2}-9y+6x\right)-3x^{2}\right)$$

Combine -9y and 6y to get -3y.

$$8x^{2}-\left(-6x^{2}-3y-2x+4x-\left(2x^{2}-9y+6x\right)-3x^{2}\right)$$

Combine -2x and 4x to get 2x.

$$8x^{2}-\left(-6x^{2}-3y+2x-\left(2x^{2}-9y+6x\right)-3x^{2}\right)$$

To find the opposite of 2x^{2}-9y+6x, find the opposite of each term.

$$8x^{2}-\left(-6x^{2}-3y+2x-2x^{2}+9y-6x-3x^{2}\right)$$

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

$$8x^{2}-\left(-8x^{2}-3y+2x+9y-6x-3x^{2}\right)$$

Combine -3y and 9y to get 6y.

$$8x^{2}-\left(-8x^{2}+6y+2x-6x-3x^{2}\right)$$

Combine 2x and -6x to get -4x.

$$8x^{2}-\left(-8x^{2}+6y-4x-3x^{2}\right)$$

Combine -8x^{2} and -3x^{2} to get -11x^{2}.

$$8x^{2}-\left(-11x^{2}+6y-4x\right)$$

To find the opposite of -11x^{2}+6y-4x, find the opposite of each term.

$$8x^{2}+11x^{2}-6y+4x$$

Combine 8x^{2} and 11x^{2} to get 19x^{2}.

$$19x^{2}-6y+4x$$