Solve (4m^{4}+6m^{3}+4m^2+9m+1)-(4m^4+2m^3+2m^2+8m+1)

$$( 4 m ^ { 4 } + 6 m ^ { 3 } + 4 m ^ { 2 } + 9 m + 1 ) - ( 4 m ^ { 4 } + 2 m ^ { 3 } + 2 m ^ { 2 } + 8 m + 1 )$$

Evaluate

$$m\left(4m^{2}+2m+1\right)$$

Solution Steps

To find the opposite of 4m^{4}+2m^{3}+2m^{2}+8m+1, find the opposite of each term.

$$4m^{4}+6m^{3}+4m^{2}+9m+1-4m^{4}-2m^{3}-2m^{2}-8m-1$$

Combine 4m^{4} and -4m^{4} to get 0.

$$6m^{3}+4m^{2}+9m+1-2m^{3}-2m^{2}-8m-1$$

Combine 6m^{3} and -2m^{3} to get 4m^{3}.

$$4m^{3}+4m^{2}+9m+1-2m^{2}-8m-1$$

Combine 4m^{2} and -2m^{2} to get 2m^{2}.

$$4m^{3}+2m^{2}+9m+1-8m-1$$

Combine 9m and -8m to get m.

$$4m^{3}+2m^{2}+m+1-1$$

Subtract 1 from 1 to get 0.

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

Expand

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

Solution Steps

To find the opposite of 4m^{4}+2m^{3}+2m^{2}+8m+1, find the opposite of each term.

$$4m^{4}+6m^{3}+4m^{2}+9m+1-4m^{4}-2m^{3}-2m^{2}-8m-1$$

Combine 4m^{4} and -4m^{4} to get 0.

$$6m^{3}+4m^{2}+9m+1-2m^{3}-2m^{2}-8m-1$$

Combine 6m^{3} and -2m^{3} to get 4m^{3}.

$$4m^{3}+4m^{2}+9m+1-2m^{2}-8m-1$$

Combine 4m^{2} and -2m^{2} to get 2m^{2}.

$$4m^{3}+2m^{2}+9m+1-8m-1$$

Combine 9m and -8m to get m.

$$4m^{3}+2m^{2}+m+1-1$$

Subtract 1 from 1 to get 0.

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