A bioinformatician computes genetic variance and must compute \( (x + 2y)^2 \) given that \( x + y = 5 \) and \( x - y = 1 \). What is the value?
["Bioinformatics Meets Algebra: Computing Genetic Variance Through Equation Solving", "In the rapidly evolving field of bioinformatics, professionals often bridge biology with computational analysis to uncover genetic patterns, identify mutations, and understand hereditary traits. A key part of this process involves processing complex genetic data—sometimes requiring intensive mathematical computations to extract meaningful insights.", "This article explores how a bioinformatician might perform seemingly abstract algebraic calculations—like expanding and evaluating ((x + 2y)^2)—within the context of genetic analysis. While real-world bioinformatics uses advanced algorithms and machine learning, simple mathematical transformations remain foundational for preprocessing data, normalizing values, and validating models.", "### Solving the Algebraic Challenge: ((x + 2y)^2) Given (x + y = 5) and (x - y = 1)", "To determine ((x + 2y)^2), we first solve for (x) and (y) using the given equations:", "[\n\begin{cases}\nx + y = 5 \\nx - y = 1\n\end{cases}\n]", "Step 1: Add the two equations", "[\n(x + y) + (x - y) = 5 + 1 \Rightarrow 2x = 6 \Rightarrow x = 3\n]", "Step 2: Substitute (x = 3) into (x + y = 5)", "[\n3 + y = 5 \Rightarrow y = 2\n]", "Step 3: Compute (x + 2y)", "[\nx + 2y = 3 + 2(2) = 3 + 4 = 7\n]", "Step 4: Square the result", "[\n(x + 2y)^2 = 7^2 = 49\n]", "---", "### Why This Matters in Bioinformatics", "While this example is algebraic, it exemplifies the kind of precise computation bioinformaticians perform daily—whether scaling gene expression values, adjusting for population variables, or normalizing sequencing data. Understanding such operations ensures accurate downstream analysis, from identifying genetic variance in cohorts to validating statistical models of inheritance.", "### Final Answer", "[\n\boxed{49}\n]", "Next time you encounter genetic variance calculations—whether in real research or abstract modeling—remember: strong foundational math powers precise biological discovery."]
