Square Identities
Square identities are standard expansions for (a+b)^2, (a-b)^2, and (a+b)(a-b) used to simplify products quickly.
Practice This ConceptMain explanation
Teacher explanation
The three main square identities are (a+b)^2=a^2+2ab+b^2, (a-b)^2=a^2-2ab+b^2, and (a+b)(a-b)=a^2-b^2. They save time because the middle term and signs can be written by pattern recognition.
Example
(x+5)^2 = x^2+10x+25 and (3p-2)^2 = 9p^2-12p+4.
Simple analogy
Square of binomial gives first square, double product, last square.
Common confusion
Students often write (a-b)^2 as a^2-b^2, forgetting the middle term -2ab.
Exam tip
For a square of a binomial, always write three terms; for sum multiplied by difference, write two terms.
Study the square identities diagram carefully
Use the labelled diagram to keep square identities clear in short answers and revision.
What this diagram makes clear
This diagram keeps the labels and direction of square identities in the right order.
Where this helps in exams
Use this for labelled diagram work and short exam answers on square identities.
Revision cue
Revise square identities through the labels before writing the answer.
Answer writing and exam use
1-mark use
Write the exact meaning of square identities in one clean line.
2-mark use
Define square identities and add one example or condition.
3-mark use
Explain square identities, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
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