3(t^2 + 4) - 2t(3t + 2) = 3t^2 + 12 - (6t^2 + 4t) = -3t^2 - 4t + 12
["How to Simplify the Algebraic Expression: Step-by-Step Breakdown of 3(t² + 4) – 2t(3t + 2) = –3t² – 4t + 12", "Understanding algebraic simplification is essential in math, and today, we’ll walk through one of the most common transformations: simplifying an expression using the distributive property and combining like terms.", "The Problem:\nWe want to simplify:\n3(t² + 4) – 2t(3t + 2) = –3t² – 4t + 12", "---", "### Step 1: Expand Each Term Using the Distributive Property", "We start by applying the distributive property to each part of the expression to eliminate the parentheses.", "1. Expand 3(t² + 4):\n $$\n 3 \cdot t² + 3 \cdot 4 = 3t² + 12\n $$", "2. Expand –2t(3t + 2):\n $$\n -2t \cdot 3t + (-2t) \cdot 2 = -6t² – 4t\n $$", "Now, combining both expansions:\n$$\n3t² + 12 – 6t² – 4t\n$$", "---", "### Step 2: Combine Like Terms", "Next, group and simplify the resulting terms:", "- Combine 3t² – 6t² = –3t²\n- The –4t remains as is\n- The constant is +12", "Putting it all together:\n$$\n–3t² – 4t + 12\n$$", "---", "### Final Expression", "So, we have shown step-by-step that:\n3(t² + 4) – 2t(3t + 2) simplifies to –3t² – 4t + 12", "---", "### Why This Matters", "Simplifying expressions is a foundational skill in algebra. It’s essential for solving equations, graphing functions, and understanding higher-level math. This particular problem demonstrates the use of:", "- Distributive property\n- Combining like terms", "Mastering these techniques helps build confidence and accuracy in math.", "---", "Pro Tip: Always verify your simplification by substituting a value for ( t ) (like ( t = 2 )) into both the original and simplified expressions — they should yield the same result.", "---", "Keywords: algebra simplification, distributive property, combine like terms, polynomial simplification, solving algebraically, step-by-step math help, expanding expressions, simplify quadratic expressions", "Meta Description:\nLearn how to simplify the expression 3(t² + 4) – 2t(3t + 2) into –3t² – 4t + 12 using distributive property and combining like terms. Step-by-step breakdown for clear understanding.", "---", "Tags: #Algebra #MathSimplification #Polynomials #QuadraticExpressions #StudentMathHelp #HighSchoolMath"]
