Solve (2r+4r^2-4r^3)-(5r^2-7r+3r^3)

$$( 2 r + 4 r ^ { 2 } - 4 r ^ { 3 } ) - ( 5 r ^ { 2 } - 7 r + 3 r ^ { 3 } )$$

Evaluate

$$r\left(9-r-7r^{2}\right)$$

Solution Steps

To find the opposite of 5r^{2}-7r+3r^{3}, find the opposite of each term.

$$2r+4r^{2}-4r^{3}-5r^{2}+7r-3r^{3}$$

Combine 4r^{2} and -5r^{2} to get -r^{2}.

$$2r-r^{2}-4r^{3}+7r-3r^{3}$$

Combine 2r and 7r to get 9r.

$$9r-r^{2}-4r^{3}-3r^{3}$$

Combine -4r^{3} and -3r^{3} to get -7r^{3}.

$$9r-r^{2}-7r^{3}$$

Expand

$$9r-r^{2}-7r^{3}$$

Solution Steps

To find the opposite of 5r^{2}-7r+3r^{3}, find the opposite of each term.

$$2r+4r^{2}-4r^{3}-5r^{2}+7r-3r^{3}$$

Combine 4r^{2} and -5r^{2} to get -r^{2}.

$$2r-r^{2}-4r^{3}+7r-3r^{3}$$

Combine 2r and 7r to get 9r.

$$9r-r^{2}-4r^{3}-3r^{3}$$

Combine -4r^{3} and -3r^{3} to get -7r^{3}.

$$9r-r^{2}-7r^{3}$$