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

$$\frac { 1 } { 2 } ( 2 - 2 m ) ^ { 2 } + \frac { 1 } { 2 } m ^ { 2 } =$$

Evaluate

$$\frac{5m^{2}}{2}-4m+2$$

Solution Steps

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

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

Use the distributive property to multiply \frac{1}{2} by 4-8m+4m^{2}.

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

Combine 2m^{2} and \frac{1}{2}m^{2} to get \frac{5}{2}m^{2}.

$$2-4m+\frac{5}{2}m^{2}$$

Expand

$$\frac{5m^{2}}{2}-4m+2$$

Solution Steps

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

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

Use the distributive property to multiply \frac{1}{2} by 4-8m+4m^{2}.

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

Combine 2m^{2} and \frac{1}{2}m^{2} to get \frac{5}{2}m^{2}.

$$2-4m+\frac{5}{2}m^{2}$$