Algebra Class: Collecting Like Terms and Adding/Subtracting

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)