Solve (7p^3-8p+5)-(3p^3+4p^2-2p+8)

$$( 7 p ^ { 3 } - 8 p + 5 ) - ( 3 p ^ { 3 } + 4 p ^ { 2 } - 2 p + 8 )$$

Evaluate

$$4p^{3}-4p^{2}-6p-3$$

Solution Steps

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

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

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

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

Combine -8p and 2p to get -6p.

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

Subtract 8 from 5 to get -3.

$$4p^{3}-6p-3-4p^{2}$$

Expand

$$4p^{3}-4p^{2}-6p-3$$

Solution Steps

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

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

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

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

Combine -8p and 2p to get -6p.

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

Subtract 8 from 5 to get -3.

$$4p^{3}-6p-3-4p^{2}$$