Expand the product \((x + 4)(x - 5)\).
["Expand the Product ((x + 4)(x - 5)): Step-by-Step Guide to Multiplying Binomials", "Expanding algebraic expressions is a fundamental skill in math, and one of the most common tasks is multiplying binomials like ((x + 4)(x - 5)). Whether you're solving equations, simplifying expressions, or preparing for higher-level math, knowing how to expand binomials accurately and efficiently is essential. In this article, we’ll explore step-by-step instructions on how to expand ((x + 4)(x - 5)), explain the logic behind the process, and highlight why mastering this skill matters.", "---", "### What Is the Product Expansion?", "The expression ((x + 4)(x - 5)) is a product of two binomials — expressions with two terms each. Multiplying them expands the product into a simpler polynomial, written as a sum of like terms. The process uses the distributive property (also known as the FOIL method for binomials), where each term in the first bracket multiplies every term in the second bracket.", "---", "### Step-by-Step Expansion of ((x + 4)(x - 5))", "1. Apply the distributive property (FOIL method):\n Multiply each term in the first binomial ((x + 4)) by each term in the second binomial ((x - 5)).\n - (x \cdot x = x^2)\n - (x \cdot (-5) = -5x)\n - (4 \cdot x = 4x)\n - (4 \cdot (-5) = -20)", "2. Write all partial products:\n Combine these results:\n [\n (x)(x) + (x)(-5) + (4)(x) + (4)(-5) = x^2 - 5x + 4x - 20\n ]", "3. Combine like terms:\n Combine the (-5x) and (+4x) terms:\n [\n x^2 - 5x + 4x - 20 = x^2 - x - 20\n ]", "---", "### Final Result", "[\n(x + 4)(x - 5) = x^2 - x - 20\n]", "This is the expanded form of the original expression — a quadratic polynomial in standard form, where the terms are ordered by descending powers of (x).", "---", "### Why Expand Binomial Products?", "- Simplifies solving equations: Expanded forms make it easier to collect terms and solve quadratic equations.\n- Facilitates graphing: Writing a function in standard form (ax^2 + bx + c) helps identify key features like zeros and vertex.\n- Strengthens algebraic fluency: Regular practice prepares students for calculus, linear algebra, and complex polynomial operations.", "---", "### Tips for Quick Expansion", "- Use the area model or grid method: Visual learners can draw a rectangle divided by ((x + 4)) and ((x - 5)) to help spot each term.\n- Remember distributive property: Never skip multiplying every term!\n- Combine like terms carefully: This step eliminates errors and ensures accuracy.\n- Check your work: Plug in a value for (x) (e.g., (x = 0) or (x = 1)) into both the original and expanded forms to verify equivalence.", "---", "### Let’s Master ((x + 4)(x - 5)): Conclusion", "Expanding ((x + 4)(x - 5)) gives (x^2 - x - 20), a crucial step in algebra that unlocks deeper understanding and problem-solving capability. By mastering the distributive property and combining like terms, you build a strong foundation for working with polynomials and beyond. Keep practicing — algebra rewards persistence with clarity and confidence.", "---", "Keywords for SEO:\nexpand ((x + 4)(x - 5)), binomial expansion, algebraic multiplication, how to expand binomials, step-by-step product of binomials, algebra tutorial, simplify ((x + 4)(x - 5)), quadratic expansion, distribute binomials.", "---", "Meta Title:\nHow to Expand ((x + 4)(x - 5)): Step-by-Step Algebra Guide", "Meta Description:\nLearn to expand ((x + 4)(x - 5)) with clear, detailed steps using the distributive property. Perfect for students mastering algebra and polynomial expressions."]
