What you need to know
Algebra becomes more reliable when every operation is applied to the whole expression and each line has a clear purpose. Focus on balancing equations, factorising accurately and making the required variable the subject of a formula.
- Solve linear and more complex equations with balanced operations.
- Rearrange formulae by undoing operations in a logical order.
- Distinguish an equation, an identity and an expression.
- Factorise as the reverse of expansion.
Key mathematics
Identity notation
\equiv
An identity is true for every permitted value of the variable.Difference of two squares
a^2-b^2=(a-b)(a+b)
A common factorisation pattern.Worked example
Make $x$ the subject of $y=\frac{3x-2}{5}$. Multiply by 5: $5y=3x-2$. Add 2 and divide by 3: $$x=\frac{5y+2}{3}.$$
EXAM TECHNIQUE
Exam tips
- Show one algebraic change per line when rearranging complicated formulae.
- After factorising, expand mentally or on paper to check the result.
- Use brackets whenever an operation applies to more than one term.
WATCH OUT
Common mistakes
- Changing the sign of only one term when moving a bracketed expression.
- Cancelling terms across addition or subtraction.
- Treating an identity as if it needs solving for a single value.
Frequently asked questions
What is the difference between an equation and an identity?
An equation is true for particular values; an identity is true for every permitted value.
How can I check a rearranged formula?
Substitute simple numerical values into the original and rearranged versions and confirm they agree.
When is factorising useful?
It helps solve equations, simplify expressions and reveal algebraic structure.