Only like terms can be collected
Like terms have the same letters raised to the same powers, e.g. and , or and . Add or subtract their number parts (coefficients) and keep the letter part unchanged: . Unlike terms such as and , or and , cannot be combined.
Multiply every term inside a single bracket
To expand , multiply the outside term by each term inside: . Keep careful track of signs, e.g. . Watch the powers: , not .
Index laws for algebra: add, subtract, multiply the powers
For the same base: (multiply → add powers), (divide → subtract), and (power of a power → multiply). Also and .
Drawn from real examiner reports.
Multiplying the powers instead of adding them
When multiplying powers of the same base the indices should be added, but students often multiply them — e.g. writing instead of , or making the same slip inside an index equation.
Sign slips when substituting a negative number
Forgetting that a negative number squared is positive, or dropping a minus sign, e.g. evaluating at as instead of , or mishandling when is negative. Putting the substituted value in brackets, , prevents this.
Not using brackets when writing or substituting into an expression
Omitting brackets changes the meaning, so at becomes (which is ) — easy to get wrong without brackets. Examiners explicitly advise using brackets when forming and evaluating expressions.
Substitute with brackets and work one operation at a time
When a formula or expression is given, write the value in brackets, then apply powers and multiplications before adding/subtracting (BIDMAS). This is exactly the method examiners reward for substitution questions, e.g. into a volume formula.
Find the value of x² when x = -3.
Simplify .
