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

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

Evaluate

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

Solution Steps

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

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

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

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

Add 1 and 1 to get 2.

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

Combine 2m and -2m to get 0.

$$2+m^{2}+m^{2}$$

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

$$2+2m^{2}$$

Expand

$$2m^{2}+2$$

Solution Steps

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

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

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

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

Add 1 and 1 to get 2.

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

Combine 2m and -2m to get 0.

$$2+m^{2}+m^{2}$$

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

$$2+2m^{2}$$