Breaking It Down: Expanding and Simplifying Expressions

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Learn how to expand and simplify algebraic expressions step by step! In this video, we’ll cover:
✅ What “expand” means in algebra
✅ How to use the distributive property
✅ Combining like terms to simplify
✅ Examples and practice problems

Perfect for students, teachers, and anyone learning algebra.
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Key topics covered include:
Combining like terms for simplification: The video starts with examples of simplifying expressions by combining terms with the same variables and powers (0:15).
Example 1: `5x - 6x + 22 - 23` simplifies to `-x - 1` (0:33-1:14).
Example 2: `x + 6x + 3y + 4y` simplifies to `7x + 7y` (1:17-1:47).
Example 3: `6xy - 2yx + 13x - 5x` simplifies to `4xy + 8x`, emphasizing that `xy` and `yx` are like terms (1:58-4:21).
Example 4: Simplifying an expression with six terms by grouping `x`, `y`, and `z` terms (4:22-5:27).
Adding pairs of expressions: The video demonstrates how to find the sum of two algebraic expressions by combining their like terms.
Example 1: Adding `2x + 4y` and `-5y` results in `2x - y` (5:28-5:59).
Rules for writing terms in algebra: The instructor explains the standard practice of writing the numerical coefficient first, followed by variables in alphabetical order (6:00-7:34).
Example: `7yx` should preferably be written as `7xy` (6:36-6:40).
Expanding expressions: The video moves on to expanding expressions, which involves using the distributive property.
Expanding expressions with a negative sign outside the parenthesis, changing the signs of the terms inside (10:30-11:13).
Expanding expressions with a number outside the parenthesis (11:13-11:38).
Expanding expressions with a negative number outside the parenthesis, requiring both multiplication and sign flipping (11:40-13:08).
Expanding expressions with multiple variables (13:10-15:06).
Expanding and simplifying combined: The video concludes with examples that involve both expanding and then simplifying the resulting expressions by combining like terms (15:10-18:40).