Solve (alpha+beta)^2-2alphabeta

$$( \alpha + \beta ) ^ { 2 } - 2 \alpha \beta$$

Evaluate

$$\alpha ^{2}+\beta ^{2}$$

Solution Steps

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

$$\alpha ^{2}+2\alpha \beta +\beta ^{2}-2\alpha \beta$$

Combine 2\alpha \beta and -2\alpha \beta to get 0.

$$\alpha ^{2}+\beta ^{2}$$

Expand

$$\alpha ^{2}+\beta ^{2}$$

Solution Steps

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

$$\alpha ^{2}+2\alpha \beta +\beta ^{2}-2\alpha \beta$$

Combine 2\alpha \beta and -2\alpha \beta to get 0.

$$\alpha ^{2}+\beta ^{2}$$