Combining Like Terms
Combining Like Terms is a core algebraic skill where terms with the same variable and exponent are grouped and simplified by adding or subtracting their coefficients, covered in Yoshiwara Elementary Algebra Chapter 5: Exponents and Roots. For Grade 6 students, this means recognizing that 8x² - 3x² = 5x², while unlike terms such as x² and x cannot be combined. This skill is used constantly in simplifying polynomials, solving equations, and working with any algebraic expression.
Key Concepts
Property We can combine like powers of the same variable. When we add like terms, we do not alter the exponent; only the coefficient of the power changes. For example: $$8x^2 3x^2 = 5x^2$$ Different powers of the same variable are not like terms and cannot be combined. For example, $8x^2 3x$ cannot be simplified.
Examples The terms $7a^3$ and $4a^3$ are like terms, so they can be combined: $7a^3 4a^3 = 3a^3$.
The expression $5w^2 + 3w^3$ cannot be simplified because $w^2$ and $w^3$ are not like terms.
Common Questions
What does combining like terms mean?
It means adding or subtracting terms that have the same variable and the same exponent. Only the coefficients change — the variable part stays the same.
Can you combine x² and x?
No. x² and x are not like terms because their exponents differ (2 vs. 1). Only terms with identical variable parts can be combined.
How do you combine like terms step by step?
Identify terms with the same variable and exponent, group them together, then add or subtract their coefficients. Leave unlike terms as they are.
Where is combining like terms in Yoshiwara Elementary Algebra?
It is taught in Chapter 5: Exponents and Roots of Yoshiwara Elementary Algebra.
Why is combining like terms important in algebra?
It simplifies expressions to their most reduced form, making equations easier to solve and polynomials easier to work with.