The parts of an expression: terms, coefficients and constants
Discover Mathematics P6: Term 1, Unit 3, Lessons 1–2
GoalName the terms, coefficients, constants and like terms in an expression.
New words
term · one part of an expression, separated from the others by + or −coefficient · the number that multiplies the letter in a termconstant · a term with no letter; its value never changeslike terms · terms with the same letter, like 3x and 5x
Explanation
An expression is built from terms joined by + or −. In 4x + 9 there are two terms: 4x and 9. In the term 4x, the number 4 is the coefficient, because it multiplies the variable x. The term 9 has no letter, so it is a constant. A letter alone, like x, has coefficient 1, because x = 1x. Like terms have the same letter, so 3x and 5x are like terms, but 3x and 5y are not. Constants are also like each other. Like terms can be added together, which we use in later lessons.
In 4x + 9
What it is
4x
a term; 4 is the coefficient and x is the variable
9
a constant term (no letter)
+
joins the two terms
Worked examples
Term
Coefficient
Variable
4a
4
a
9
—
—
Parts of 4a + 9. Terms: 4a and 9. Coefficient: 4. Variable: a. Constant: 9.
Term
2x
3y
x
8
Coefficient
2
3
1
—
Look at 2x + 3y + x + 8. There are four terms: 2x, 3y, x and 8. The coefficients are 2, 3 and 1 (for x). The constant is 8. The like terms are 2x and x, because both have the letter x.
Group
Terms
m-terms
5m, 2m
Constants
3, 7
n-terms
4n
Sorting terms: 5m, 3, 2m, 7 and 4n. The m-terms are 5m and 2m, the constants are 3 and 7, and 4n is alone.
Class activity
Expression cards. Write terms on small cards: 3x, 8, 5x, 2y, 6, x. A grown-up shuffles them and the child sorts them into piles of like terms, then makes an expression by laying cards in a row with plus signs between them. Count the terms, name the constant and read each coefficient aloud.
Practice
1
In 7y + 2 name the coefficient, the variable and the constant.
Coefficient 7, variable y, constant 2.
2
How many terms does 3x + 4y + 5 have? Name them.
Three terms: 3x, 4y and 5.
3
Which are the like terms in 6a + 2b + 4a + 9?
6a and 4a (both have the letter a).
4
What is the coefficient of x in x + 6?
1, because x = 1x.
5
Are 5x and 5y like terms? Explain.
No. They have different letters. The coefficients can be the same, but the letters must match.
