Using perfect square identities

2026-11-26Algebraic Manipulation Mr Yip

Recognise and expand (a±b)² without missing the middle term.

Key formulas

(a \pm b)^{2} = a^{2} \pm 2ab + b^{2}

What this lesson covers

This lesson builds Secondary 2–3 skill in perfect square identity. Read the key formulas, study the worked example, then attempt the written practice and the four-question MCQ review.

Method

Write every step. Name the rule you use (perfect square identity) before substituting numbers. Keep units and signs visible until the final sentence.

Common mistakes

Students often rush the sign, use the wrong percentage base, or cancel terms instead of factors. Pause after each line and ask whether the step is reversible.

Exam habit

Underline the question verb (simplify, solve, factorise, find). Box the final answer and, where sensible, substitute back for a quick check.

Worked example

Worked example — perfect square identity

Problem. Apply the method for perfect square identity with the numbers 4 and 3.

Solution. Identify the rule for perfect square identity. Substitute 4 and 3 carefully with signs in brackets if needed. Complete each operation on a new line. State the final answer clearly and check by reversing one step.

Review quiz

1 / 4

Warm-up on perfect square identity: what is 6+6?

Practice questions

Practice 1 on perfect square identity: compute with the value 34.
Practice 2 on perfect square identity: change the numbers and repeat the same method.
Practice 3 on perfect square identity: write one sentence explaining the key rule.
Practice 4 on perfect square identity: invent a similar exam-style question and solve it.

Study notes

What is the main idea of perfect square identity?

Apply the stated formula or rule with clear steps, then check by reversing or substituting.

How should I revise this topic?

Cover the worked example, redo the practice without notes, then complete the MCQ set and log any wrong options.