Solution: First expand $ (2x - 3)(x + 4) $:
["SEO-Optimized Article: How to Expand the Expression $ (2x - 3)(x + 4) $: Step-by-Step Guide", "Expanding algebraic expressions is a foundational skill in mathematics, especially in algebra. One of the most common tasks students encounter is expanding products like $ (2x - 3)(x + 4) $. Understanding how to expand such binomials not only boosts your problem-solving skills but also aids in solving equations, simplifying complex expressions, and mastering quadratic equations. In this article, we’ll walk you through the step-by-step process of expanding $ (2x - 3)(x + 4) $, explain the concepts involved, and highlight why this skill matters in mathematics.", "---", "### Why Expand $ (2x - 3)(x + 4) $?", "Before diving into the solution, let’s understand the significance:\nExpanding allows us to transform a factored expression into a readable polynomial form. This process reveals the expression’s true structure, making it easier to evaluate values, compare expressions, or solve for variables. For example, expanding helps in:", "- Simplifying equations before solving\n- Identifying coefficients and degrees in polynomials\n- Serving as a basis for factoring and quadratic applications", "---", "### Step-by-Step Expansion of $ (2x - 3)(x + 4) $", "We use the distributive property (also known as the FOIL method for binomials) to expand the expression.", "Step 1: Identify the terms in each binomial\nFirst binomial: $ 2x - 3 $\nSecond binomial: $ x + 4 $", "Step 2: Apply the distributive property\nMultiply each term in the first binomial by each term in the second binomial:", "$$\n(2x - 3)(x + 4) = 2x \cdot x + 2x \cdot 4 - 3 \cdot x - 3 \cdot 4\n$$", "Step 3: Perform the multiplications\nCalculate each product:", "- $ 2x \cdot x = 2x^2 $\n- $ 2x \cdot 4 = 8x $\n- $ -3 \cdot x = -3x $\n- $ -3 \cdot 4 = -12 $", "Step 4: Write all terms together\nCombine all products:", "$$\n2x^2 + 8x - 3x - 12\n$$", "Step 5: Combine like terms\nMerge the $ 8x $ and $ -3x $ terms:", "$$\n2x^2 + 5x - 12\n$$", "---", "### Final Result: $ (2x - 3)(x + 4) = 2x^2 + 5x - 12 $", "This is the fully expanded form of the expression. From here, you can now:", "- Solve equations like $ 2x^2 + 5x - 12 = 0 $ using factoring or the quadratic formula\n- Graph the corresponding quadratic function\n- Use in real-world applications such as projectile motion or profit modeling", "---", "### Tips to Master Expansion", "- Always distribute fully — forgetfulness leads to missing terms.\n- Label each multiplication step to avoid confusion.\n- Combine like terms carefully — this step is essential for simplifying expressions.\n- Use color-coding or grouping for clarity, especially in classroom or self-study settings.", "---", "### Conclusion", "Expanding $ (2x - 3)(x + 4) $ is a simple yet powerful exercise in algebra. By following the distributive property step-by-step, combining like terms, and reviewing your work, you build confidence and precision—key traits for success in higher-level math. Keep practicing, and watch how this skill unlocks more advanced topics with ease.", "Related SEO Keywords:\nExpand $ (2x - 3)(x + 4) $, algebraic expansion tutorial, how to expand binomials, solve $ (2x - 3)(x + 4) = 0 $, polynomial multiplication, algebra fundamentals.", "Meta Description for SEO:\nLearn how to expand $ (2x - 3)(x + 4) $ step-by-step using the distributive property. This simple algebra technique builds a strong foundation for solving equations and mastering quadratic expressions. Step-by-step guide included.", "---", "Tags: #Algebra #MathTips #ExpandPolynomials #LearnAlgebra #Equations #MathEducation #HighSchoolMath"]
