Calculator Soup Combining Like Terms with Negative Coefficients

What Are Like Terms?

Like terms are terms in an algebraic expression that have the same variable raised to the same power. For example, in the expression 3x + 5y - 2x, the terms 3x and -2x are like terms because they both contain the variable x with the same exponent (1).

The coefficients of like terms can be positive or negative. When combining like terms, you add or subtract their coefficients while keeping the variable part unchanged.

Combining Like Terms with Negative Coefficients

When combining like terms with negative coefficients, follow these steps:

1. Identify all like terms in the expression.
2. Add or subtract their coefficients.
3. Keep the variable part the same.
4. Simplify the resulting expression.

Negative coefficients can make combining terms seem more complicated, but the process remains the same as with positive coefficients.

Step-by-Step Example

Let's combine like terms in the expression: 7y - 4y + 2y - 5y

1. Identify all y terms: 7y, -4y, +2y, -5y
2. Add the coefficients: 7 + (-4) + 2 + (-5) = 0
3. Combine: 0y = 0
4. Final simplified form: 0

Common Mistakes

When combining like terms with negative coefficients, students often make these mistakes:

• Forgetting to change the sign when subtracting negative coefficients
• Miscounting the number of terms or their coefficients
• Not simplifying the final expression completely

Double-checking each step helps prevent these errors.

Real-World Applications

Combining like terms with negative coefficients is used in:

• Physics equations involving forces in opposite directions
• Economics models with positive and negative contributions
• Chemistry calculations with reactants and products

Understanding this concept helps in solving real-world problems involving opposing quantities.