Explain the Hardy-Weinberg principle using an algebraic equation.

(N/A) The Hardy-Weinberg principle states that allele frequencies in a population are stable and remain constant from generation to generation. The gene pool (total genes and their alleles in a population) remains constant,which is called genetic equilibrium.
In a diploid organism,let the frequency of allele $A$ be $p$ and the frequency of allele $a$ be $q$.
The sum of all allele frequencies is $1$,so $p + q = 1$.
The frequency of individuals with genotype $AA$ is $p^2$,the frequency of individuals with genotype $aa$ is $q^2$,and the frequency of individuals with genotype $Aa$ is $2pq$.
Thus,the algebraic equation is $p^2 + 2pq + q^2 = 1$,which is the expansion of $(p + q)^2 = 1$.
When the measured allele frequencies differ from the expected values,it indicates evolutionary change. Disturbance in genetic equilibrium or Hardy-Weinberg equilibrium is interpreted as the result of evolutionary change in a population.