Solve (p+3)*(p-1)*(p-3)-(p+1)-2p

$$( p + 3 ) \cdot ( p - 1 ) \cdot ( p - 3 ) - ( p + 1 ) - 2 p$$

Evaluate

$$p^{3}-p^{2}-12p+8$$

Solution Steps

Apply the distributive property by multiplying each term of p+3 by each term of p-1.

$$\left(p^{2}-p+3p-3\right)\left(p-3\right)-\left(p+1\right)-2p$$

Combine -p and 3p to get 2p.

$$\left(p^{2}+2p-3\right)\left(p-3\right)-\left(p+1\right)-2p$$

Apply the distributive property by multiplying each term of p^{2}+2p-3 by each term of p-3.

$$p^{3}-3p^{2}+2p^{2}-6p-3p+9-\left(p+1\right)-2p$$

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

$$p^{3}-p^{2}-6p-3p+9-\left(p+1\right)-2p$$

Combine -6p and -3p to get -9p.

$$p^{3}-p^{2}-9p+9-\left(p+1\right)-2p$$

To find the opposite of p+1, find the opposite of each term.

$$p^{3}-p^{2}-9p+9-p-1-2p$$

Combine -9p and -p to get -10p.

$$p^{3}-p^{2}-10p+9-1-2p$$

Subtract 1 from 9 to get 8.

$$p^{3}-p^{2}-10p+8-2p$$

Combine -10p and -2p to get -12p.

$$p^{3}-p^{2}-12p+8$$

Expand

$$p^{3}-p^{2}-12p+8$$

Solution Steps

Apply the distributive property by multiplying each term of p+3 by each term of p-1.

$$\left(p^{2}-p+3p-3\right)\left(p-3\right)-\left(p+1\right)-2p$$

Combine -p and 3p to get 2p.

$$\left(p^{2}+2p-3\right)\left(p-3\right)-\left(p+1\right)-2p$$

Apply the distributive property by multiplying each term of p^{2}+2p-3 by each term of p-3.

$$p^{3}-3p^{2}+2p^{2}-6p-3p+9-\left(p+1\right)-2p$$

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

$$p^{3}-p^{2}-6p-3p+9-\left(p+1\right)-2p$$

Combine -6p and -3p to get -9p.

$$p^{3}-p^{2}-9p+9-\left(p+1\right)-2p$$

To find the opposite of p+1, find the opposite of each term.

$$p^{3}-p^{2}-9p+9-p-1-2p$$

Combine -9p and -p to get -10p.

$$p^{3}-p^{2}-10p+9-1-2p$$

Subtract 1 from 9 to get 8.

$$p^{3}-p^{2}-10p+8-2p$$

Combine -10p and -2p to get -12p.

$$p^{3}-p^{2}-12p+8$$