Collect like terms, keeping their signs, then multiply and divide algebraic terms such as 3a × 4b and 12x³y ÷ 4x.
What you will learn
- Collect like terms, keeping their signs
- Multiply terms such as 3a × 4b
- Divide terms such as 12x³y ÷ 4x
Like terms
Like terms have exactly the same letters and powers: 3a and −5a, or 2x² and x².
Add their numbers; the letters stay the same.
- 5a + 3b − 2a + b
- a terms: 5a − 2a = 3a
- b terms: 3b + b = 4b
- = 3a + 4b
The sign belongs to the term after it. x² and x are not like terms, and neither are 3x and 3. Number terms collect with each other: 6y − 2 − 9y + 7 = −3y + 5. A total of −1a is written −a: 2a − 3a = −a.
To collect x² terms and x terms: 5x² + 2x − 3x² − 6x = 2x² − 4x. The perimeter of a triangle with sides 2x + 1, 3x − 4 and x + 6 is 2x + 3x + x + 1 − 4 + 6 = 6x + 3.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Like terms
- Multiplying and dividing
7 practice questions, marked as you go; about 20 minutes in all.
Key terms
Like terms
In this unit: Algebraic expressions
The language of algebra: writing and substituting into expressions, simplifying, expanding brackets, factorising, and telling expressions, equations, formulae and identities apart.