Solve 8x^2-{3x^2-2[3y-3(x^2-5y)-(5x^2+6y)]}=

$$8 x ^ { 2 } - \{ 3 x ^ { 2 } - 2 [ 3 y - 3 ( x ^ { 2 } - 5 y ) - ( 5 x ^ { 2 } + 6 y ) ] \} =$$

Evaluate

$$24y-11x^{2}$$

Solution Steps

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

$$8x^{2}-\left(3x^{2}-2\left(3y-3x^{2}+15y-\left(5x^{2}+6y\right)\right)\right)$$

Combine 3y and 15y to get 18y.

$$8x^{2}-\left(3x^{2}-2\left(18y-3x^{2}-\left(5x^{2}+6y\right)\right)\right)$$

To find the opposite of 5x^{2}+6y, find the opposite of each term.

$$8x^{2}-\left(3x^{2}-2\left(18y-3x^{2}-5x^{2}-6y\right)\right)$$

Combine -3x^{2} and -5x^{2} to get -8x^{2}.

$$8x^{2}-\left(3x^{2}-2\left(18y-8x^{2}-6y\right)\right)$$

Combine 18y and -6y to get 12y.

$$8x^{2}-\left(3x^{2}-2\left(12y-8x^{2}\right)\right)$$

Use the distributive property to multiply -2 by 12y-8x^{2}.

$$8x^{2}-\left(3x^{2}-24y+16x^{2}\right)$$

Combine 3x^{2} and 16x^{2} to get 19x^{2}.

$$8x^{2}-\left(19x^{2}-24y\right)$$

To find the opposite of 19x^{2}-24y, find the opposite of each term.

$$8x^{2}-19x^{2}+24y$$

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

$$-11x^{2}+24y$$

Expand

$$24y-11x^{2}$$

Solution Steps

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

$$8x^{2}-\left(3x^{2}-2\left(3y-3x^{2}+15y-\left(5x^{2}+6y\right)\right)\right)$$

Combine 3y and 15y to get 18y.

$$8x^{2}-\left(3x^{2}-2\left(18y-3x^{2}-\left(5x^{2}+6y\right)\right)\right)$$

To find the opposite of 5x^{2}+6y, find the opposite of each term.

$$8x^{2}-\left(3x^{2}-2\left(18y-3x^{2}-5x^{2}-6y\right)\right)$$

Combine -3x^{2} and -5x^{2} to get -8x^{2}.

$$8x^{2}-\left(3x^{2}-2\left(18y-8x^{2}-6y\right)\right)$$

Combine 18y and -6y to get 12y.

$$8x^{2}-\left(3x^{2}-2\left(12y-8x^{2}\right)\right)$$

Use the distributive property to multiply -2 by 12y-8x^{2}.

$$8x^{2}-\left(3x^{2}-24y+16x^{2}\right)$$

Combine 3x^{2} and 16x^{2} to get 19x^{2}.

$$8x^{2}-\left(19x^{2}-24y\right)$$

To find the opposite of 19x^{2}-24y, find the opposite of each term.

$$8x^{2}-19x^{2}+24y$$

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

$$-11x^{2}+24y$$