When is the correct use of algebraic identities most useful?

Correct answer: When an expression has to be expanded, simplified or factorised quickly

The direct answer is A: algebraic identities are most useful when an expression must be expanded, simplified, or factorised quickly. An identity is a rule that remains true for all allowed values of its variables. For example, \((a+b)^2=a^2+2ab+b^2\), \((a-b)^2=a^2-2ab+b^2\), and \(a^2-b^2=(a-b)(a+b)\). The method is simple: first compare the expression with a known identity, match the terms, and then apply the rule carefully. This saves time and reduces repeated multiplication. Option A is correct because these are exactly the main uses of identities. Option B, colouring a figure, is an artistic activity and does not require algebraic identities. Option C, saying there is no term, is not a meaningful use; identities work with algebraic terms and expressions. Option D is wrong because identities do not remove mathematical symbols; they rearrange or transform expressions while preserving their value. Memory cue: “recognise the pattern, apply the identity, check by expansion.”