Solve (-5m^{3}+2m+5m^{2}+2m^4)-(-2m+8m^2-6m^4-2m^3)

$$( - 5 m ^ { 3 } + 2 m + 5 m ^ { 2 } + 2 m ^ { 4 } ) - ( - 2 m + 8 m ^ { 2 } - 6 m ^ { 4 } - 2 m ^ { 3 } )$$

Evaluate

$$m\left(8m^{3}-3m^{2}-3m+4\right)$$

Solution Steps

To find the opposite of -2m+8m^{2}-6m^{4}-2m^{3}, find the opposite of each term.

$$-5m^{3}+2m+5m^{2}+2m^{4}+2m-8m^{2}+6m^{4}+2m^{3}$$

Combine 2m and 2m to get 4m.

$$-5m^{3}+4m+5m^{2}+2m^{4}-8m^{2}+6m^{4}+2m^{3}$$

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

$$-5m^{3}+4m-3m^{2}+2m^{4}+6m^{4}+2m^{3}$$

Combine 2m^{4} and 6m^{4} to get 8m^{4}.

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

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

$$-3m^{3}+4m-3m^{2}+8m^{4}$$

Expand

$$8m^{4}-3m^{3}-3m^{2}+4m$$

Solution Steps

To find the opposite of -2m+8m^{2}-6m^{4}-2m^{3}, find the opposite of each term.

$$-5m^{3}+2m+5m^{2}+2m^{4}+2m-8m^{2}+6m^{4}+2m^{3}$$

Combine 2m and 2m to get 4m.

$$-5m^{3}+4m+5m^{2}+2m^{4}-8m^{2}+6m^{4}+2m^{3}$$

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

$$-5m^{3}+4m-3m^{2}+2m^{4}+6m^{4}+2m^{3}$$

Combine 2m^{4} and 6m^{4} to get 8m^{4}.

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

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

$$-3m^{3}+4m-3m^{2}+8m^{4}$$