Solve (4r^3-5r^4+3)-(6-4r^3)+(7-2r^2

$$( 4 r ^ { 3 } - 5 r ^ { 4 } + 3 ) - ( 6 - 4 r ^ { 3 } ) + ( 7 - 2 r ^ { 2 }$$

Evaluate

$$4-2r^{2}+8r^{3}-5r^{4}$$

Solution Steps

To find the opposite of 6-4r^{3}, find the opposite of each term.

$$4r^{3}-5r^{4}+3-6+4r^{3}+7-2r^{2}$$

Subtract 6 from 3 to get -3.

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

Combine 4r^{3} and 4r^{3} to get 8r^{3}.

$$8r^{3}-5r^{4}-3+7-2r^{2}$$

Add -3 and 7 to get 4.

$$8r^{3}-5r^{4}+4-2r^{2}$$

Expand

$$4-2r^{2}+8r^{3}-5r^{4}$$

Solution Steps

To find the opposite of 6-4r^{3}, find the opposite of each term.

$$4r^{3}-5r^{4}+3-6+4r^{3}+7-2r^{2}$$

Subtract 6 from 3 to get -3.

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

Combine 4r^{3} and 4r^{3} to get 8r^{3}.

$$8r^{3}-5r^{4}-3+7-2r^{2}$$

Add -3 and 7 to get 4.

$$8r^{3}-5r^{4}+4-2r^{2}$$