Compute the square of \( (3x - 2) \).
["# Compute the Square of ( (3x - 2) ): A Step-by-Step Algebra Guide", "Understanding how to compute the square of a binomial expression like ( (3x - 2)^2 ) is a fundamental skill in algebra. Whether you're solving equations, graphing functions, or simplifying expressions, knowing how to expand and simplify squared binomials is essential. In this article, we’ll walk through the process of squaring ( (3x - 2) ), explain the formula behind it, and provide clear steps with real-world context to strengthen your algebraic abilities.", "## What Does It Mean to Compute the Square of a Binomial?", "The square of a binomial refers to the operation of multiplying the same binomial expression by itself:\n[\n(a - b)^2 \quad \ ext{or} \quad (a + b)^2\n]\nExpanding ( (3x - 2)^2 ) means multiplying ( (3x - 2)(3x - 2) ), and applying the algebraic identity:", "[\n(a - b)^2 = a^2 - 2ab + b^2\n]", "This formula allows you to efficiently expand expressions involving squared terms without performing brute-force multiplication.", "## Step-by-Step Calculation of ( (3x - 2)^2 )", "Let’s compute ( (3x - 2)^2 ) step by step.", "### Step 1: Apply the binomial squaring formula\nUsing ( (a - b)^2 = a^2 - 2ab + b^2 ), where ( a = 3x ) and ( b = 2 ):\n[\n(3x - 2)^2 = (3x)^2 - 2(3x)(2) + (2)^2\n]", "### Step 2: Compute each term\n- ( (3x)^2 = 9x^2 )\n- ( 2(3x)(2) = 12x )\n- ( (2)^2 = 4 )", "### Step 3: Substitute back and simplify\n[\n(3x - 2)^2 = 9x^2 - 12x + 4\n]", "This is the fully expanded, simplified form of ( (3x - 2)^2 ).", "## Why Is This Important?", "Knowing how to square a binomial like ( (3x - 2) ) has practical applications across math and science:", "- Quadratic equations: Simplifying expressions before solving.\n- Graphing parabolas: The standard form ( y = a(x - h)^2 + k ) relies on squaring binomials.\n- Physics and engineering: Calculating distances or forces involving linear expressions.\n- Computer graphics and machine learning: Quadratic models are frequently used for fitting curves and optimizing functions.", "## Expanded Form Summary", "[\n(3x - 2)^2 = 9x^2 - 12x + 4\n]", "- Leading term: ( 9x^2 ) — the square of the coefficient of ( x )\n- Middle term: ( -12x ) — the negative twice-product of the two terms\n- Constant term: ( +4 ) — the square of the constant", "## Tips to Remember", "- Always use the identity ( (a - b)^2 = a^2 - 2ab + b^2 ) for efficiency.\n- Watch signs carefully: ( -2ab = -2(a)(b) ), so distributing the negative matters.\n- Practice with different coefficients and constants to build speed and accuracy.", "## Conclusion", "Computing the square of ( (3x - 2) ) is a straightforward application of the binomial expansion formula. By understanding and applying the identity ( (a - b)^2 = a^2 - 2ab + b^2 ), learners can quickly simplify and expand such expressions with confidence. Whether for homework, exams, or real-world problem-solving, mastering this technique strengthens foundational algebra and opens doors to more advanced mathematics.", "---", "Keywords: compute the square of (3x - 2), expand (3x - 2)², binomial square formula, algebra tutorial, step-by-step expansion, polynomial identities, quadratic expressions, algebra practice."]
