Question: Compute the square of $ 3\sqrt{2} - 2\sqrt{3} $.
["Title: How to Compute the Square of $ 3\sqrt{2} - 2\sqrt{3} $: Step-by-Step Guide", "Meta Description:\nLearn how to compute the square of $ 3\sqrt{2} - 2\sqrt{3} $ using the algebraic formula $ (a - b)^2 = a^2 - 2ab + b^2 $. Simplify this expression step-by-step for accurate results.", "---", "### Introduction\nMathematics often involves manipulating expressions with radicals, and one common operation is squaring a binomial expression like $ 3\sqrt{2} - 2\sqrt{3} $. Knowing how to compute the square of such an expression helps in algebra, calculus, and problem-solving. In this article, we’ll explore how to compute the square of $ 3\sqrt{2} - 2\sqrt{3} $, break down each step clearly, and provide the simplified result.", "### Understanding the Expression\nWe want to compute:\n$$\n(3\sqrt{2} - 2\sqrt{3})^2\n$$", "This is a binomial square, and the algebraic identity to use is:\n$$\n(a - b)^2 = a^2 - 2ab + b^2\n$$", "Here:\n- $ a = 3\sqrt{2} $\n- $ b = 2\sqrt{3} $", "### Step 1: Square Each Term\nFirst, compute $ a^2 = (3\sqrt{2})^2 $:\n$$\n(3\sqrt{2})^2 = 3^2 \cdot (\sqrt{2})^2 = 9 \cdot 2 = 18\n$$", "Next, compute $ b^2 = (2\sqrt{3})^2 $:\n$$\n(2\sqrt{3})^2 = 2^2 \cdot (\sqrt{3})^2 = 4 \cdot 3 = 12\n$$", "### Step 2: Compute the Cross Term\nNow, calculate $ -2ab = -2 \cdot (3\sqrt{2}) \cdot (2\sqrt{3}) $:\n$$\n-2ab = -2 \cdot 3 \cdot 2 \cdot \sqrt{2} \cdot \sqrt{3} = -12 \cdot \sqrt{6}\n$$", "(Note: $ \sqrt{2} \cdot \sqrt{3} = \sqrt{6} $)", "### Step 3: Combine All Terms\nNow add the results:\n$$\n(3\sqrt{2} - 2\sqrt{3})^2 = 18 - 12\sqrt{6} + 12\n$$", "Combine the constant terms:\n$$\n18 + 12 = 30\n$$", "So the final simplified expression is:\n$$\n30 - 12\sqrt{6}\n$$", "### Conclusion\nComputing the square of $ 3\sqrt{2} - 2\sqrt{3} $ follows straightforward algebraic steps using $ (a - b)^2 = a^2 - 2ab + b^2 $. The result is $ 30 - 12\sqrt{6} $, which combines rational and irrational parts neatly. Mastering this process enhances your algebraic manipulation skills and is essential for advanced math topics.", "---", "### Key Takeaways\n- Use $ (a - b)^2 = a^2 - 2ab + b^2 $ for binomial squares.\n- Square coefficients and radicals using $ (k\sqrt{m})^2 = k^2 \cdot m $.\n- Multiply radicals using $ \sqrt{a} \cdot \sqrt{b} = \sqrt{ab} $.\n- Always combine constant and radical terms where possible.", "---", "Keywords for SEO:\ncompute square of $ 3\sqrt{2} - 2\sqrt{3} $, square radical expression, algebra tutorial, simplify radical expressions, $ (a - b)^2 $ calculation, $ (3\sqrt{2} - 2\sqrt{3})^2 $, step-by-step math example", "You Might Also Like:\n- How to Simplify Radical Expressions\n- Expanding Binomials: Step-by-Step Guide\n- Best Methods to Square Binomials with Radicals"]
