The variance ${\sigma }^2$ of a random variable $X$ is given by:

The variance of a random variable $X$, denoted by $\text{Var}(X)$ or ${\sigma }^2$, measures the spread of the distribution. It is defined as the expectation of the squared deviation of $X$ from its mean $\mu =E[X]$:
$$\text{Var}(X)=E[(X-E[X]{)}^2]$$
Expanding the square:
$$\text{Var}(X)=E[X^2-2XE[X]+(E[X]{)}^2]$$
Using the linearity of expectation:
$$\text{Var}(X)=E[X^2]-2E[X]E[X]+(E[X]{)}^2$$
$$\text{Var}(X)=E[X^2]-2(E[X]{)}^2+(E[X]{)}^2$$
$$\text{Var}(X)=E[X^2]-(E[X]{)}^2$$