wunder beta🧹 Collecting Like Terms
Tidy up messy expressions by combining terms that match: 3a + 2b + 5a becomes 8a + 2b. Handle negative coefficients without losing track of the signs.
What you’ll learn
- Collecting Like TermsSimplify algebraic expressions by identifying like terms and combining their coefficients, including terms with negative coefficients, while preserving the expression's value.Like terms have the same letter part, so 3a and 5a can combine but 3a and 2b cannot. To collect them, add the coefficients and keep the letter: 3a + 5a = 8a, giving 3a + 2b + 5a = 8a + 2b. With negatives, each sign travels with its term: in 7x − 3 − 2x + 5, the x-terms give 7x − 2x = 5x and the numbers give −3 + 5 = 2, so the answer is 5x + 2. Simplifying shortens an expression without changing its value.
Questions this course answers
Which pair below are like terms?
Like terms share the same letter part; 5x and 8x are both x-terms.
Simplify 3a + 2b + 5a.
Add the a-terms: 3a + 5a = 8a. The 2b has no partner, so it stays.
When you add 3a + 5a, what happens to the letter a?
You add the coefficients (3 + 5 = 8) and keep the letter unchanged: 8a.
Simplify 7x − 3 − 2x + 5.
x-terms: 7x − 2x = 5x. Numbers: −3 + 5 = +2. So 5x + 2.
Why can't 8a and 2b be combined into a single term?
Only like terms combine; a and b are different quantities.
Grounded in trusted sources
- BBC Bitesize — Maths (Key Stage 3)
- Khan Academy — Combining like terms
- NRICH (University of Cambridge)
- Britannica
Every Wunder lesson is built from real, reputable sources — never invented.
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