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

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

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(m^{2}-2m\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

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

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

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

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

Expand

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(m^{2}-2m\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

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

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

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

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