Solve (m^{2}+m+1)(m^2-2m-2)+2m(m^2+4)-(m^2-1)(m^2-2m+2)

$$( m ^ { 2 } + m + 1 ) ( m ^ { 2 } - 2 m - 2 ) + 2 m ( m ^ { 2 } + 4 ) - ( m ^ { 2 } - 1 ) ( m ^ { 2 } - 2 m + 2 )$$

Evaluate

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

Solution Steps

Use the distributive property to multiply m^{2}+m+1 by m^{2}-2m-2 and combine like terms.

$$m^{4}-m^{3}-3m^{2}-4m-2+2m\left(m^{2}+4\right)-\left(m^{2}-1\right)\left(m^{2}-2m+2\right)$$

Use the distributive property to multiply 2m by m^{2}+4.

$$m^{4}-m^{3}-3m^{2}-4m-2+2m^{3}+8m-\left(m^{2}-1\right)\left(m^{2}-2m+2\right)$$

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

$$m^{4}+m^{3}-3m^{2}-4m-2+8m-\left(m^{2}-1\right)\left(m^{2}-2m+2\right)$$

Combine -4m and 8m to get 4m.

$$m^{4}+m^{3}-3m^{2}+4m-2-\left(m^{2}-1\right)\left(m^{2}-2m+2\right)$$

Use the distributive property to multiply m^{2}-1 by m^{2}-2m+2 and combine like terms.

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

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

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

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

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

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

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

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

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

Combine 4m and -2m to get 2m.

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

Add -2 and 2 to get 0.

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

Expand

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

Solution Steps

Use the distributive property to multiply m^{2}+m+1 by m^{2}-2m-2 and combine like terms.

$$m^{4}-m^{3}-3m^{2}-4m-2+2m\left(m^{2}+4\right)-\left(m^{2}-1\right)\left(m^{2}-2m+2\right)$$

Use the distributive property to multiply 2m by m^{2}+4.

$$m^{4}-m^{3}-3m^{2}-4m-2+2m^{3}+8m-\left(m^{2}-1\right)\left(m^{2}-2m+2\right)$$

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

$$m^{4}+m^{3}-3m^{2}-4m-2+8m-\left(m^{2}-1\right)\left(m^{2}-2m+2\right)$$

Combine -4m and 8m to get 4m.

$$m^{4}+m^{3}-3m^{2}+4m-2-\left(m^{2}-1\right)\left(m^{2}-2m+2\right)$$

Use the distributive property to multiply m^{2}-1 by m^{2}-2m+2 and combine like terms.

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

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

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

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

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

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

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

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

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

Combine 4m and -2m to get 2m.

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

Add -2 and 2 to get 0.

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