`(p_q)^(2)+2pq+q^(2)=1` represents an equation used in

Options

A. population genetics
B. Mendelian genetics
C. biometrics
D. molecular genetics

Explanation

To solve the question `(p_q)^(2)+2pq+q^(2)=1` and identify what it represents, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Equation**: The equation given is `(p + q)² + 2pq + q² = 1`. This is a mathematical expression that can be rearranged and simplified.

2. **Recognize the Components**: In this equation, `p` and `q` typically represent the frequencies of two alleles in a population. For example, `p` could represent the frequency of the dominant allele, while `q` represents the frequency of the recessive allele.

3. **Relate to Hardy-Weinberg Principle**: This equation is derived from the Hardy-Weinberg principle, which states that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of evolutionary influences.

4. **Understand the Implications**: According to the Hardy-Weinberg principle, the equation can be expanded to show the expected frequencies of the three genotypes in a population:
- Homozygous dominant (AA): \( p^2 \)
- Heterozygous (Aa): \( 2pq \)
- Homozygous recessive (aa): \( q^2 \)

5. **Conclusion**: Therefore, the equation `(p + q)² = 1` represents the conditions of a population in equilibrium, where the total frequency of alleles sums to 1. This is a fundamental concept in population genetics.

### Final Answer:
The equation `(p + q)² + 2pq + q² = 1` represents an equation used in **population genetics**, specifically illustrating the **Hardy-Weinberg principle**.

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