Combine like terms: $ 10a^2 + 35ab - 6ab - 21b^2 = 10a^2 + 29ab - 21b^2 $.
["Understanding Combine Like Terms: Simplifying the Expression $10a^2 + 35ab - 6ab - 21b^2$", "When working with algebraic expressions, one of the fundamental skills is combining like terms. This process streamlines equations and makes them easier to manipulate, solve, or analyze. In this article, we’ll explore how to simplify the expression:", "[\n10a^2 + 35ab - 6ab - 21b^2\n]", "and demonstrate why it simplifies to:", "[\n10a^2 + 29ab - 21b^2\n]", "---", "### What Are Like Terms?", "Like terms are terms in an expression that contain the same variables raised to the same powers. Only these terms can be combined. For example:", "- $35ab$ and $-6ab$ are like terms because both contain the variables $a$ and $b$ raised to the first power.\n- $10a^2$, $-21b^2$ are unlike terms and cannot be combined directly.", "---", "### Step-by-Step Simplification", "Start with the original expression:", "[\n10a^2 + 35ab - 6ab - 21b^2\n]", "#### Step 1: Identify and group like terms", "Group the $ab$ terms and leave $10a^2$ and $-21b^2$ as they are (they involve different variables):", "[\n10a^2 + (35ab - 6ab) - 21b^2\n]", "#### Step 2: Combine coefficients of like terms", "Now combine $35ab$ and $-6ab$:", "[\n35ab - 6ab = (35 - 6)ab = 29ab\n]", "So the expression becomes:", "[\n10a^2 + 29ab - 21b^2\n]", "---", "### Why This Works", "Combining like terms allows us to reduce complexity and highlight the essential parts of the polynomial. In this case, simplifying the $ab$ terms makes the expression cleaner and easier to interpret, especially when substituting values or solving equations later.", "---", "### Final Simplified Expression", "[\n10a^2 + 29ab - 21b^2\n]", "---", "### Key Takeaways", "- Like terms must contain identical variables and exponents to be combined.\n- Combining like terms simplifies algebraic expressions and supports further operations such as factoring, expanding, or solving equations.\n- Always simplify step-by-step to avoid errors.", "---", "Mastering like term combination is essential for algebra proficiency. Whether you’re simplifying equations or preparing for calculus, this foundational skill helps build clarity and confidence in working with polynomials.", "Keywords: combine like terms, algebraic simplification, polynomial simplification, algebraic expression, simplify $10a^2 + 35ab - 6ab - 21b^2$, $10a^2 + 29ab - 21b^2$\nSearch Intent: Beginners and students seeking clear explanation on combining like terms in algebra.", "---", "By applying this method consistently, expressions become easier to manage—turning complex equations into streamlined forms ready for deeper mathematical exploration."]
