Thus, the factored form is $ \boxed{(4x - 5)^2} $.
["Title: Factored Form of $ (4x - 5)^2 $: Simplifying Quadratics Made Easy", "When solving quadratic equations or working with polynomials, one of the most essential skills is factoring. A common expression students encounter is $ (4x - 5)^2 $, which is already presented in its factored form. But what does this truly mean, and why is factoring it important?", "In algebra, factoring transforms a completed square expression into its original multiplicative components. The factored form $ (4x - 5)^2 $ reveals key insights: it shows two identical binomial factors, indicating the quadratic touches the x-axis at exactly one point—a repeated root. This confirms the equation $ (4x - 5)^2 = 0 $ has a double root at $ x = \frac{5}{4} $.", "But beyond theory, understanding the factored form $ (4x - 5)^2 $ streamlines simplifying, expanding, and solving quadratic equations. For instance, expanding $ (4x - 5)^2 $ using the binomial square formula $ (a - b)^2 = a^2 - 2ab + b^2 $ gives:", "[\n(4x)^2 - 2(4x)(5) + 5^2 = 16x^2 - 40x + 25\n]", "This matches the expanded standard form $ 16x^2 - 40x + 25 $, validating the accuracy of the factored version.", "In practical applications, knowing when an expression like $ (4x - 5)^2 $ appears allows for faster simplification in calculus, optimization, and real-world modeling. Whether simplifying rational expressions or analyzing parabolas, recognizing factorized forms leads to clearer problem-solving paths.", "Conclusion:\nThe factored form $ \boxed{(4x - 5)^2} $ is more than notation—it’s a gateway to deeper understanding and efficient computation in algebra. Mastering this skill empowers learners to tackle more complex equations and enhance mathematical fluency.", "---", "Keywords for SEO: factored form of $ (4x - 5)^2 $, algebraic factoring, solving quadratics, expanding binomials, solving $ (4x - 5)^2 = 0 $, algebra tutorial, polynomial factorization, simplified quadratic expressions."]
