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Questions and Answers
What is the result of combining like terms in the expression 3x + 2x + x?
What is the simplified form of the expression 2a + 3c + 5a?
What is the result of simplifying the expression 4x^2 + 2x^2 + 3x^2?
What is the simplified form of the expression 5w + 2w - 3w?
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What is the result of simplifying the expression xy + 3xy + 2xy?
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What is the simplified form of the expression 3a + 2c + 5a - 2c?
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Study Notes
Collecting Like Terms
- In algebra, collecting like terms means combining terms with the same variable (e.g., a + a + a = 3a)
- Example: a + a + a + a = 4a (because a + a is 2a, and 2a + a is 3a, and 3a + a is 4a)
- Another example: 3c + 2c = 5c (because 3 times c plus 2 times c is 5 times c)
Adding/Subtracting Terms
- When adding or subtracting terms, only combine like terms (e.g., 3x + 2x = 5x, but x + y is just x + y)
- Example: w + w = 2w (not 2 + w, because w on its own is like 1w)
Simplifying Expressions
- To simplify expressions, combine like terms (e.g., 2x + 3x = 5x)
- Example: a + c cannot be simplified because a and c are different variables
- Another example: xy + 4xy = 5xy (because xy is a single term)
- However, x + y cannot be simplified because x and y are different variables
More Examples
- x^2 + x^2 = 2x^2 (because x^2 is a single term)
- 5c + 5c - 12c = -2c (because 5c + 5c is 10c, and 10c - 12c is -2c)
- x + x + 2x + 5 + 3 = 4x + 8 (because x + x + 2x is 4x, and 5 + 3 is 8)
- 4a + 2c + 5a + 9c = 9a + 11c (because 4a + 5a is 9a, and 2c + 9c is 11c)
More Examples (Simplifying Expressions)
- 8a + 7w + 2w - 3a = 5a + 9w (because 8a - 3a is 5a, and 7w + 2w is 9w)
- 6s + 4t - 8s - 5t = -2s - t (because 6s - 8s is -2s, and 4t - 5t is -t)
- 10x - 5y - x - 2y = 9x - 7y (because 10x - x is 9x, and -5y - 2y is -7y)
- 4x^2 + 8x^2 = 12x^2 (because 4x^2 + 8x^2 is 12x^2)
- -5v + 8v = 3v (because -5v + 8v is 3v)
Collecting Like Terms
- Combining terms with the same variable (e.g., a + a + a = 3a)
- Example: a + a + a + a = 4a (because a + a is 2a, and 2a + a is 3a, and 3a + a is 4a)
Adding/Subtracting Terms
- Only combine like terms when adding or subtracting (e.g., 3x + 2x = 5x, but x + y is just x + y)
- Example: w + w = 2w (not 2 + w, because w on its own is like 1w)
Simplifying Expressions
- Combine like terms to simplify expressions (e.g., 2x + 3x = 5x)
- Example: a + c cannot be simplified because a and c are different variables
- Example: xy + 4xy = 5xy (because xy is a single term)
- Example: x + y cannot be simplified because x and y are different variables
Examples
- x^2 + x^2 = 2x^2 (because x^2 is a single term)
- 5c + 5c - 12c = -2c (because 5c + 5c is 10c, and 10c - 12c is -2c)
- x + x + 2x + 5 + 3 = 4x + 8 (because x + x + 2x is 4x, and 5 + 3 is 8)
- 4a + 2c + 5a + 9c = 9a + 11c (because 4a + 5a is 9a, and 2c + 9c is 11c)
More Examples
- 8a + 7w + 2w - 3a = 5a + 9w (because 8a - 3a is 5a, and 7w + 2w is 9w)
- 6s + 4t - 8s - 5t = -2s - t (because 6s - 8s is -2s, and 4t - 5t is -t)
- 10x - 5y - x - 2y = 9x - 7y (because 10x - x is 9x, and -5y - 2y is -7y)
- 4x^2 + 8x^2 = 12x^2 (because 4x^2 + 8x^2 is 12x^2)
- -5v + 8v = 3v (because -5v + 8v is 3v)
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Description
Learn about collecting like terms in algebra, combining terms with the same variable, and rules for adding and subtracting terms in algebraic expressions.
