Algebraic Expressions and Identities
Focused last-minute revision with key concepts, formulas, worked examples, exam traps and practice.
Chapter Snapshot
- Like terms have exactly the same variable part.
- Only like terms combine by addition or subtraction.
- Multiplication distributes over addition and subtraction.
- The identities (a+b)², (a-b)² and (a+b)(a-b) are essential.
- Identities can simplify numerical calculations.
What You Will Learn
- Identify terms, factors and coefficients
- Combine like terms
- Multiply monomials and polynomials
- Use distributive law
- Apply standard algebraic identities
Last-Minute Chapter Map
Use this chapter in three passes:
- Understand the core ideas.
- Memorise formulas and exam traps.
- Attempt the compact practice set without looking at the answers.
Terms and coefficients
In 5x²y - 3xy + 7, the terms are 5x²y, -3xy and 7. Coefficients are numerical factors attached to variable terms. Like terms have identical variable parts including powers.
Addition and subtraction
Combine only like terms. For example 3x + 5x - 2 = 8x - 2. Terms such as x and x² are unlike.
Multiplication
Multiply coefficients and variable factors, then use the distributive property for expressions with brackets.
Identities
Identities are equalities true for all permitted values. They are useful both for expansion and factorisation.
Formula Sheet
Formula / Key Relations
(a+b)²
Do not forget the middle term.
(a-b)²
The last term remains positive.
Difference of squares
Useful for expansion and factorisation.
General binomials
Useful for mental multiplication.
Worked Examples
Use (a+b)².
Choose a convenient base.
Exam Traps
Quick Revision
Quick Revision
- Like terms have exactly the same variable part.
- Only like terms combine by addition or subtraction.
- Multiplication distributes over addition and subtraction.
- The identities (a+b)², (a-b)² and (a+b)(a-b) are essential.
- Identities can simplify numerical calculations.
- Revise the formula sheet once more before attempting questions.
Compact Practice
4x + 3x = ?
View Solution
7x
Expand (x-4)².
View Solution
x² - 8x + 16
(a+b)(a-b) = ?
View Solution
a² - b²
Find 103² using an identity.
View Solution
10609
Final Chapter Summary
Chapter Summary
- Like terms have exactly the same variable part.
- Only like terms combine by addition or subtraction.
- Multiplication distributes over addition and subtraction.
- The identities (a+b)², (a-b)² and (a+b)(a-b) are essential.
- Identities can simplify numerical calculations.
- Prioritise correct method, clean working and final units where applicable.