2
Terms, coefficients and like terms: simplifying by combining
Mathematics Prep 1 Term 1, Unit 2, Lesson 1
GoalName the terms, coefficients and constant of an expression and simplify by collecting like terms.
New words
term · a number, a letter, or a product of them, like 3xcoefficient · the number multiplying the letter in a termconstant term · a term with no letter, like 7like terms · terms with the same letters and the same powers
Explanation
The terms of an expression are the parts separated by + and −. In 4x² − 3x + 7 the terms are 4x², −3x and 7. The coefficient is the number in front of the letters: 4 in 4x², −3 in −3x. A bare x has coefficient 1. The term 7 has no letter and is the constant term. Like terms have the same letters with the same powers: 2xy and 5xy are like terms, but 3x² and 3x are not. We can add and subtract only like terms, by adding their coefficients: 2x + 3x = 5x. Never change the letter part: x + x = 2x, not x².
★Remember
Add or subtract only like terms: the letters and their powers must match.
Worked examples
| Term | Coefficient | Kind |
|---|---|---|
| 4x² | 4 | variable term |
| −3x | −3 | variable term |
| 7 | — | constant term |
Like or unlike? 2xy, 5xy and −xy are like terms (same letters xy). 3x² and 3x are unlike, because the powers differ. 4a and 4b are unlike, because the letters differ.
Simplify 5x + 2y − 3x + 4y + 6. Collect the x terms: 5x − 3x = 2x. Collect the y terms: 2y + 4y = 6y. The constant stays 6. The result is 2x + 6y + 6.
Class activity
Term sort. With a grown-up, write eight terms such as 3x, 5y, 2x, 7, −4y, x², 6, −x on cards. Sort them into like-term piles. Then add each pile.
Practice
1
Write the coefficient of −5y and of x.
−5 and 1.
2
Which is a like term of 3ab: 5ab, 3a or 3b?
5ab, because it has the same letters ab.
3
Simplify 6x + 4x.
10x.
4
Simplify 8a + 3b − 5a + b.
3a + 4b.
5
Mina simplifies 3x + 4x² as 7x³. What is wrong?
3x and 4x² are not like terms, so they cannot be combined. It stays 3x + 4x².