Solve (5m^{2}+2m^{3}-13m^{4})-(-12m^{4}+3m^3+10m^5)-(4m^4+12m^3)

$$( 5 m ^ { 2 } + 2 m ^ { 3 } - 13 m ^ { 4 } ) - ( - 12 m ^ { 4 } + 3 m ^ { 3 } + 10 m ^ { 5 } ) - ( 4 m ^ { 4 } + 12 m ^ { 3 } )$$

Evaluate

$$-m^{2}\left(10m^{3}+5m^{2}+13m-5\right)$$

Solution Steps

To find the opposite of -12m^{4}+3m^{3}+10m^{5}, find the opposite of each term.

$$5m^{2}+2m^{3}-13m^{4}+12m^{4}-3m^{3}-10m^{5}-\left(4m^{4}+12m^{3}\right)$$

Combine -13m^{4} and 12m^{4} to get -m^{4}.

$$5m^{2}+2m^{3}-m^{4}-3m^{3}-10m^{5}-\left(4m^{4}+12m^{3}\right)$$

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

$$5m^{2}-m^{3}-m^{4}-10m^{5}-\left(4m^{4}+12m^{3}\right)$$

To find the opposite of 4m^{4}+12m^{3}, find the opposite of each term.

$$5m^{2}-m^{3}-m^{4}-10m^{5}-4m^{4}-12m^{3}$$

Combine -m^{4} and -4m^{4} to get -5m^{4}.

$$5m^{2}-m^{3}-5m^{4}-10m^{5}-12m^{3}$$

Combine -m^{3} and -12m^{3} to get -13m^{3}.

$$5m^{2}-13m^{3}-5m^{4}-10m^{5}$$

Expand

$$5m^{2}-13m^{3}-5m^{4}-10m^{5}$$

Solution Steps

To find the opposite of -12m^{4}+3m^{3}+10m^{5}, find the opposite of each term.

$$5m^{2}+2m^{3}-13m^{4}+12m^{4}-3m^{3}-10m^{5}-\left(4m^{4}+12m^{3}\right)$$

Combine -13m^{4} and 12m^{4} to get -m^{4}.

$$5m^{2}+2m^{3}-m^{4}-3m^{3}-10m^{5}-\left(4m^{4}+12m^{3}\right)$$

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

$$5m^{2}-m^{3}-m^{4}-10m^{5}-\left(4m^{4}+12m^{3}\right)$$

To find the opposite of 4m^{4}+12m^{3}, find the opposite of each term.

$$5m^{2}-m^{3}-m^{4}-10m^{5}-4m^{4}-12m^{3}$$

Combine -m^{4} and -4m^{4} to get -5m^{4}.

$$5m^{2}-m^{3}-5m^{4}-10m^{5}-12m^{3}$$

Combine -m^{3} and -12m^{3} to get -13m^{3}.

$$5m^{2}-13m^{3}-5m^{4}-10m^{5}$$