Solve (m-2)(m^2+4m+4)-2m(m^2-3)

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

Evaluate

$$-m^{3}+2m^{2}+2m-8$$

Solution Steps

Use the distributive property to multiply m-2 by m^{2}+4m+4 and combine like terms.

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

Use the distributive property to multiply -2m by m^{2}-3.

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

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

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

Combine -4m and 6m to get 2m.

$$-m^{3}+2m^{2}+2m-8$$

Expand

$$-m^{3}+2m^{2}+2m-8$$

Solution Steps

Use the distributive property to multiply m-2 by m^{2}+4m+4 and combine like terms.

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

Use the distributive property to multiply -2m by m^{2}-3.

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

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

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

Combine -4m and 6m to get 2m.

$$-m^{3}+2m^{2}+2m-8$$