Algebraic Expressions — Year 7 Revision Notes
These notes cover using letters for unknowns, writing and simplifying expressions by collecting like terms, and substituting numbers into expressions.
Writing expressions and notation
In algebra we write 3 × a as 3a, and a × a as a². The number in front of a letter is the coefficient. An expression such as 2n + 5 means 'double a number and add 5'.
Key Facts & Formulas
- 3 × a = 3a
- a × a = a²
- a ÷ b = a/b
Tips
- Do not write the multiplication sign in algebra — 3a, not 3 × a.
- Read questions carefully: 'two more than n' is n + 2.
Collecting like terms
Like terms contain exactly the same letters. Add or subtract their coefficients to simplify. So 3a + 5a = 8a, and 4x + 2y − x = 3x + 2y. You cannot combine unlike terms such as 3a and 2b.
Key Facts & Formulas
- 3a + 5a = 8a
- 4x + 2y − x = 3x + 2y
Tips
- Keep the + or − sign attached to the term in front of it.
- x and x² are not like terms and cannot be combined.
Substitution
Substituting means replacing each letter with a number and working out the value. If a = 4 and b = −2, then 3a + b = 3 × 4 + (−2) = 10. Remember that 3a means 3 × a.
Key Facts & Formulas
- if a = 4, 3a = 12
Tips
- Put brackets around negative numbers when you substitute them.
- Follow the order of operations: do multiplication before addition.
Revision Checklist
- I can write an expression from a description
- I can use correct algebra notation (3a, a²)
- I can simplify by collecting like terms
- I can substitute positive and negative numbers into an expression
Frequently Asked Questions
Why is a × a equal to a² and not 2a?
2a means a + a (two lots of a), while a² means a × a (a multiplied by itself). They are different, so keep them separate.
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