Like terms
Identify and combine like terms in Grade 9 algebra by recognizing matching variable parts and exponents, then adding or subtracting their coefficients to simplify expressions.
Key Concepts
Property Like terms, such as $ 8x^4$ and $x^4$, have the same variables raised to the same powers.
Examples The terms $7a^2b$ and $ 2a^2b$ are like terms because their variable part, $a^2b$, is identical. The terms $4x^3y^2$ and $4x^2y^3$ are NOT like terms. The exponents on $x$ and $y$ are different. To simplify $(4x^2 + 6x) + (3x^2 2x)$, you combine the like terms $4x^2$ and $3x^2$, and then $6x$ and $ 2x$.
Explanation Imagine like terms are identical twins in the algebra world. They must have the exact same variables with the exact same exponents—their 'variable DNA' has to be a perfect match! The numbers in front (coefficients) can be different, but that's it. Only these identical twins can be combined when you add or subtract polynomials.
Common Questions
What are like terms in algebra?
Like terms are terms that have the same variable(s) raised to the same power(s). For example, 5x and -3x are like terms, and 4x² and 7x² are like terms, but 3x and 3x² are NOT because the exponents differ.
How do you combine like terms?
Add or subtract the numerical coefficients while keeping the variable part unchanged. For example, 5x + (-3x) = 2x, and 4x² + 7x² = 11x². Only the coefficients change; the variable and exponent stay the same.
Can you combine terms with different variables?
No. Terms must have identical variable parts to be like terms. 3x and 3y cannot be combined because they have different variables. Similarly, 2xy and 2x cannot be combined because one has an extra y factor.