Solve (1-m)^2(1+m)^2

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

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1-m\right)^{2}.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(1+m\right)^{2}.

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

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

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

Expand

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1-m\right)^{2}.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(1+m\right)^{2}.

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

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

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