Collecting like terms
Collecting like terms in Grade 8 Saxon Math Course 3 is the process of combining all terms with the same variable and exponent in an algebraic expression to simplify it. Students identify like terms, add or subtract their coefficients, and write the simplified expression. This skill is the foundation of all algebraic simplification and equation solving.
Key Concepts
Property We combine or 'collect' like terms by adding their numerical coefficients. The variables do not change.
Examples $3x + 2 x + 3 = (3x x) + (2 + 3) = 2x + 5$ $2a^2 + 3b a^2 4b = (2a^2 a^2) + (3b 4b) = a^2 b$ $3x + 2xy + xy x = (3x x) + (2xy + xy) = 2x + 3xy$.
Explanation Think of collecting like terms as sorting your laundry. You can only combine socks with socks and shirts with shirts. In algebra, you combine terms with the exact same variable part, like 'x' with 'x' or 'ab' with 'ab'. The number in front, the coefficient, just tells you how many of each item you have collected.
Common Questions
What does collecting like terms mean in algebra?
Collecting like terms means identifying terms with the same variable and exponent, then adding or subtracting their coefficients to simplify the expression.
What are like terms in an algebraic expression?
Like terms have identical variable parts (same variable raised to the same power). For example, 3x and -5x are like terms; 3x and 3x squared are not.
How do you collect like terms in 4x + 3y - 2x + y?
Group x terms: 4x - 2x = 2x. Group y terms: 3y + y = 4y. Simplified: 2x + 4y.
Can you collect a variable term and a constant term?
No. Variables and constants are not like terms. 5x + 3 cannot be combined further because one has a variable part and the other is a plain number.
How does Saxon Math Course 3 use collecting like terms?
Saxon Math Course 3 uses this skill throughout equation solving, requiring students to simplify expressions on each side before applying inverse operations to isolate the variable.