Algebra words
- A term is a single number, letter or product, such as 3x or 5ab. An expression is a group of terms, such as 3x + 2y − 5.
- An equation has an equals sign and can be solved, such as 3x + 2 = 11. A formula links quantities, such as V = IR.
- An identity is true for every value of the variable, shown with ≡, such as 2(x + 3) ≡ 2x + 6.
Notation
- 3x means 3 × x; ab means a × b; x² means x × x; 4x² means 4 × x × x.
- a/b means a ÷ b. Write numbers before letters, and letters in alphabetical order: 3ab, not b3a.
Collecting like terms
- Like terms have exactly the same letters and powers: 3x and −x are like terms; 3x and 3x² are not.
- 3x + 2y − x + 5y = 2x + 7y. Keep the sign in front of each term with it.
Multiplying and dividing
- Multiply the numbers, then the letters: 2a × 3b = 6ab; 4x × 2x = 8x².
- Use index laws for powers: 3a²b × 4ab³ = 12a³b⁴.
- Divide the numbers, then cancel letters: 12x² ÷ 4x = 3x; 18xy ÷ 6y = 3x.
Key terms
- Term
- A single number, letter or product, such as 5x.
- Expression
- A collection of terms with no equals sign.
- Equation
- A statement with an equals sign that is true for particular values.
- Formula
- A rule linking two or more quantities, such as A = lw.
- Identity
- A statement that is true for all values, shown with ≡.
- Like terms
- Terms with the same letters and powers, which can be collected.
- Coefficient
- The number in front of a letter, such as 3 in 3x.