Factorisation Using Identities
Factorisation using identities means rewriting an expression as a product by matching it with a known algebraic identity.
Practice This ConceptMain explanation
Teacher explanation
Many expressions look difficult until the pattern is recognised. For example, x^2+10x+25 matches a^2+2ab+b^2, so it becomes (x+5)^2. The skill is to compare terms carefully before selecting the identity.
Example
9a^2-25 = (3a)^2-5^2 = (3a-5)(3a+5).
Simple analogy
Pattern first, identity next, factor last.
Common confusion
Students often choose an identity only by seeing two square terms and ignore the middle term condition.
Exam tip
Before factorising a three-term expression as a perfect square, check whether the middle term is exactly twice the product of the square roots.
Answer writing and exam use
1-mark use
Write the exact meaning of factorisation using identities in one clean line.
2-mark use
Define factorisation using identities and add one example or condition.
3-mark use
Explain factorisation using identities, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
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