Solve 3x^2-(x^2+xy-[x(x^2-y)-y(2x-3y)]+5xy)-4y^2

$$3 x ^ { 2 } - ( x ^ { 2 } + x y - [ x ( x ^ { 2 } - y ) - y ( 2 x - 3 y ) ] + 5 x y ) - 4 y ^ { 2 }$$

Evaluate

$$x^{3}+2x^{2}-9xy-y^{2}$$

Solution Steps

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

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

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

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

To find the opposite of 2yx-3y^{2}, find the opposite of each term.

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

Combine -xy and -2yx to get -3xy.

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

To find the opposite of x^{3}-3xy+3y^{2}, find the opposite of each term.

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

Combine xy and 3xy to get 4xy.

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

Combine 4xy and 5xy to get 9xy.

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

To find the opposite of x^{2}+9xy-x^{3}-3y^{2}, find the opposite of each term.

$$3x^{2}-x^{2}-9xy+x^{3}+3y^{2}-4y^{2}$$

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

$$2x^{2}-9xy+x^{3}+3y^{2}-4y^{2}$$

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

$$2x^{2}-9xy+x^{3}-y^{2}$$

Expand

$$x^{3}+2x^{2}-9xy-y^{2}$$

Solution Steps

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

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

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

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

To find the opposite of 2yx-3y^{2}, find the opposite of each term.

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

Combine -xy and -2yx to get -3xy.

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

To find the opposite of x^{3}-3xy+3y^{2}, find the opposite of each term.

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

Combine xy and 3xy to get 4xy.

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

Combine 4xy and 5xy to get 9xy.

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

To find the opposite of x^{2}+9xy-x^{3}-3y^{2}, find the opposite of each term.

$$3x^{2}-x^{2}-9xy+x^{3}+3y^{2}-4y^{2}$$

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

$$2x^{2}-9xy+x^{3}+3y^{2}-4y^{2}$$

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

$$2x^{2}-9xy+x^{3}-y^{2}$$