Solve 6x^{2}+2xy+3+5(2xy-x^3+y^2-2)-3(2y^2-x^3+6xy)

$$6 x ^ { 2 } + 2 x y + 3 + 5 ( 2 x y - x ^ { 3 } + y ^ { 2 } - 2 ) - 3 ( 2 y ^ { 2 } - x ^ { 3 } + 6 x y )$$

Evaluate

$$-2x^{3}+6x^{2}-6xy-y^{2}-7$$

Solution Steps

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

$$6x^{2}+2xy+3+10xy-5x^{3}+5y^{2}-10-3\left(2y^{2}-x^{3}+6xy\right)$$

Combine 2xy and 10xy to get 12xy.

$$6x^{2}+12xy+3-5x^{3}+5y^{2}-10-3\left(2y^{2}-x^{3}+6xy\right)$$

Subtract 10 from 3 to get -7.

$$6x^{2}+12xy-7-5x^{3}+5y^{2}-3\left(2y^{2}-x^{3}+6xy\right)$$

Use the distributive property to multiply -3 by 2y^{2}-x^{3}+6xy.

$$6x^{2}+12xy-7-5x^{3}+5y^{2}-6y^{2}+3x^{3}-18xy$$

Combine 5y^{2} and -6y^{2} to get -y^{2}.

$$6x^{2}+12xy-7-5x^{3}-y^{2}+3x^{3}-18xy$$

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

$$6x^{2}+12xy-7-2x^{3}-y^{2}-18xy$$

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

$$6x^{2}-6xy-7-2x^{3}-y^{2}$$

Expand

$$-2x^{3}+6x^{2}-6xy-y^{2}-7$$

Solution Steps

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

$$6x^{2}+2xy+3+10xy-5x^{3}+5y^{2}-10-3\left(2y^{2}-x^{3}+6xy\right)$$

Combine 2xy and 10xy to get 12xy.

$$6x^{2}+12xy+3-5x^{3}+5y^{2}-10-3\left(2y^{2}-x^{3}+6xy\right)$$

Subtract 10 from 3 to get -7.

$$6x^{2}+12xy-7-5x^{3}+5y^{2}-3\left(2y^{2}-x^{3}+6xy\right)$$

Use the distributive property to multiply -3 by 2y^{2}-x^{3}+6xy.

$$6x^{2}+12xy-7-5x^{3}+5y^{2}-6y^{2}+3x^{3}-18xy$$

Combine 5y^{2} and -6y^{2} to get -y^{2}.

$$6x^{2}+12xy-7-5x^{3}-y^{2}+3x^{3}-18xy$$

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

$$6x^{2}+12xy-7-2x^{3}-y^{2}-18xy$$

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

$$6x^{2}-6xy-7-2x^{3}-y^{2}$$