Like terms
Identify and combine like terms in Grade 10 algebra by matching variables and their exponents, then add or subtract coefficients to simplify polynomial and algebraic expressions.
Key Concepts
Like terms have the same variable raised to the same power. To simplify, add the coefficients of the like terms.
Simplify: $4ab 3a + 5 7ba + 6a$. Solution: $(4ab 7ab) + ( 3a + 6a) + 5 = 3ab + 3a + 5$. Simplify: $8p^2 + 2q 5p^2 3q + 10$. Solution: $(8p^2 5p^2) + (2q 3q) + 10 = 3p^2 q + 10$.
Imagine you have a big pile of fruit. You can easily count how many apples ($x^2$) you have and how many bananas ($xy$) you have, but you cannot add them into one group of 'apple bananas'. Like terms are the same type of fruit. You can only combine things that are exactly alike to tidy up your expression!
Common Questions
What makes two algebraic terms 'like terms'?
Like terms have identical variable parts — same variables raised to exactly the same powers. For example, 5x²y and -3x²y are like terms, but 5x²y and 5xy² are not.
How do you simplify 7x²-3x+4+2x²+x-9?
Combine like terms: (7x²+2x²)+(-3x+x)+(4-9) = 9x²-2x-5.
Can constant terms be combined with variable terms?
No. Constants (like 5 or -3) are like terms only with other constants. You cannot combine 5 and 3x; they are different types of terms.