Now expand $ (2y - z)^2 $:
["# How to Expand $ (2y - z)^2 $: A Step-by-Step Guide with Formula and Examples", "Expanding binomials like $ (2y - z)^2 $ is a fundamental algebraic skill that helps in simplifying expressions, solving equations, and preparing for more advanced math topics. In this guide, we’ll explore how to expand $ (2y - z)^2 $ step-by-step, provide the resulting formula, and show practical examples to strengthen your understanding.", "---", "## What Does Expanding $ (2y - z)^2 $ Mean?", "The expression $ (2y - z)^2 $ means the square of the binomial $ (2y - z) $. Squaring a binomial follows the formula:", "$$\n(a - b)^2 = a^2 - 2ab + b^2\n$$", "When applied to $ (2y - z)^2 $, we replace $ a = 2y $ and $ b = z $, resulting in:", "$$\n(2y - z)^2 = (2y)^2 - 2(2y)(z) + (z)^2\n$$", "---", "## Step-by-Step Expansion", "1. Square the First Term:\n $$\n (2y)^2 = 4y^2\n $$", "2. Calculate the Cross Term:\n $$\n 2(2y)(z) = 4yz \quad \Rightarrow \quad -2(2y)(z) = -4yz\n $$", "3. Square the Second Term:\n $$\n (z)^2 = z^2\n $$", "4. Combine All Terms:\n Putting it all together,\n $$\n (2y - z)^2 = 4y^2 - 4yz + z^2\n $$", "---", "## Final Expanded Form", "$$\n\boxed{(2y - z)^2 = 4y^2 - 4yz + z^2}\n$$", "This expanded expression is widely used in algebra, calculus, and applied mathematics to simplify complex formulas or solve quadratic equations.", "---", "## Why Is This Expansion Important?", "- Simplifies Expressions: Helps reduce complex algebraic forms into simpler, easier-to-work-with terms.\n- Foundation for Quadratic Practice: A key step toward understanding quadratic equations $ ay^2 + byz + cz^2 $.\n- Real-World Applications: Useful in physics, engineering, and computer graphics where coordinate adjustments and transformations involve such squares.", "---", "## Practice Example: Expand $ (3x - 2w)^2 $", "Let’s test the process with $ (3x - 2w)^2 $:\n- $ a = 3x $, $ b = 2w $\n- $ (3x)^2 = 9x^2 $\n- $ -2(3x)(2w) = -12xw $\n- $ (2w)^2 = 4w^2 $", "So,\n$$\n(3x - 2w)^2 = 9x^2 - 12xw + 4w^2\n$$", "---", "## Conclusion", "Expanding $ (2y - z)^2 $ follows a simple pattern based on the binomial square rule, yielding $ 4y^2 - 4yz + z^2 $. Master this technique to enhance your algebraic proficiency and tackle more complex equations with confidence. Practice with different coefficients and terms to build intuition and mathematical fluency.", "---", "Keywords: expand $ (2y - z)^2 $, algebra tutorial, binomial expansion, algebraic identities, quadratic expressions, math practice, step-by-step explanation, high school math, learning algebra.\nMeta Description: Learn how to expand $ (2y - z)^2 $ using the binomial formula step-by-step. Get the full expanded form, practical examples, and explanations to master this essential algebra skill."]
