Identifying Like Terms in Polynomials
Identifying like terms in polynomials requires matching both the variable and its exponent exactly — a foundational skill for adding and subtracting polynomials in enVision Algebra 1 Chapter 7 for Grade 11. Terms like 3x² and -5x² are like terms (same variable, same exponent 2) and combine to -2x². But 6x² and 6x are not like terms because their exponents differ (2 vs. 1). In the expression 4y³ + 2y - 7y³ + 5y, the like terms are 4y³ and -7y³ (combining to -3y³) and 2y and 5y (combining to 7y). Only the coefficients change when like terms are combined; the variable part stays identical.
Key Concepts
• Like terms are any terms that are exactly alike in their variable factors. The exponents on the variable factors must also match.
• To combine like terms, add or subtract their coefficients while keeping the variable part unchanged.
Common Questions
What makes two terms in a polynomial like terms?
Two terms are like terms if they have exactly the same variable raised to exactly the same power. Both the variable and the exponent must match — coefficients can differ.
Are 3x² and 3x like terms?
No. Although they share the same variable x and the same coefficient 3, the exponents differ (2 vs. 1), so they are not like terms and cannot be combined.
How do you combine 3x² and -5x²?
Add their coefficients while keeping the variable part unchanged: 3x² + (-5x²) = (3 + (-5))x² = -2x².
In 4y³ + 2y - 7y³ + 5y, which terms can be combined?
4y³ and -7y³ are like terms (combine to -3y³), and 2y and 5y are like terms (combine to 7y). The simplified result is -3y³ + 7y.
Why does combining like terms only change the coefficient, not the variable?
Like terms represent the same type of quantity. Adding 3x² and -5x² is like having 3 of something and removing 5, leaving -2 of the same thing. The type (x²) does not change.