Question: Expand the product \( (2x - 3y)^2 \).
["SEO Article: Expand the Product ( (2x - 3y)^2 ) – Step-by-Step Explanation", "When learning algebra, expanding binomial expressions is a fundamental skill that helps solve equations, simplify expressions, and understand geometry and physics better. One commonly encountered expression is:", "[\n(2x - 3y)^2\n]", "This article explains in detail how to expand ( (2x - 3y)^2 ) using proven algebraic techniques. Whether you're a student preparing for exams or a teacher looking to clarify the concept, this step-by-step guide ensures you master binomial expansion with clarity and confidence.", "---", "### What Does ( (2x - 3y)^2 ) Mean?", "The expression ( (2x - 3y)^2 ) represents the square of a binomial — a binomial is a two-term expression. Squaring a binomial means multiplying the same expression by itself:", "[\n(2x - 3y)^2 = (2x - 3y)(2x - 3y)\n]", "Expanding this product requires applying the distributive property (also called the FOIL method).", "---", "### Step 1: Apply the FOIL Method", "FOIL stands for:\n- First terms\n- Outer terms\n- Inner terms\n- Last terms", "Multiply each term in the first binomial by each term in the second:", "1. First terms:\n ( 2x \ imes 2x = 4x^2 )", "2. Outer terms:\n ( 2x \ imes (-3y) = -6xy )", "3. Inner terms:\n ( -3y \ imes 2x = -6xy )", "4. Last terms:\n ( -3y \ imes (-3y) = 9y^2 )", "---", "### Step 2: Add the Products", "Now combine all the products:", "[\n(2x - 3y)^2 = 4x^2 - 6xy - 6xy + 9y^2\n]", "Combine like terms (( -6xy - 6xy = -12xy )):", "[\n(2x - 3y)^2 = 4x^2 - 12xy + 9y^2\n]", "---", "### Final Expanded Form", "[\n\boxed{ (2x - 3y)^2 = 4x^2 - 12xy + 9y^2 }\n]", "---", "### Why Expanding ( (2x - 3y)^2 ) Matters", "- Algebraic Simplification: Helps simplify complicated expressions.\n- Quadratic Equations: Essential in solving equations involving squared binomials.\n- Real-World Applications: Used in geometry (e.g., area of rectangles or squares) and physics formulas.\n- Foundation for Higher Math: Prepares students for polynomial expansions and calculus.", "---", "### Practice Problem", "Try expanding:\n[\n(3a + 4b)^2\n]", "Hint: Use the same FOIL method but with coefficients 3 and 4.\nAnswer:\n[\n(3a + 4b)^2 = 9a^2 + 24ab + 16b^2\n]", "---", "### Conclusion", "Expanding ( (2x - 3y)^2 ) follows a straightforward algebraic process using the FOIL method. By breaking it down step-by-step, recognizing the binomial pattern, and combining like terms, you gain both speed and accuracy in algebra. Mastering this skill opens the door to advanced math and real-world problem solving.", "---", "### SEO Keywords:\nexpand (2x - 3y)^2, binomial expansion, algebraic identity, FOIL method, expand squared binomial, algebra tutorial, math problem solving, quadratic expansion, expand (2x - 3y)^2", "---", "Optimizing your understanding and practice of expanding binomials like ( (2x - 3y)^2 ) ensures strong roots in algebra — essential for success in STEM fields and beyond."]
