Factorisation Using Identities
Factorisation using identities means rewriting an expression as a product by matching it with a known algebraic identity.
In one line: Pattern first, identity next, factor last.
Practice This ConceptUnderstand it
Many expressions look difficult until the pattern is recognised. For example, x2+10x+25 matches a2+2ab+b2, so it becomes (x+5)2. The skill is to compare terms carefully before selecting the identity.
Example
Formula and rule
Match a2+2ab+b2, a2-2ab+b2, a2-b2, a3+b3, or a3-b3 before factorising.
See it worked out
Follow the example line by line, then use the same method on new questions.
Worked example
Factorise 4x2+20x+25.
- 1The first and last terms are (2x)2 and 52, and the middle term is 2(2x)(5)=20x.
- 2So the factor form is (2x+5)2.
Method you can reuse
Check yourself
Answer the question in your head before opening the answer.
Try it yourself
How will you factorise x2-12x+36 using an identity?
Think first, then show answerHide answer
Common wrong answer
Writing x2+8x+16 as (x+8)2.
Why it loses marks: (x+8)2 gives x2+16x+64.
Don't mix this up
Exam tip
Write it in the exam
Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.
How CBSE asks it
- 1
Enough for 1 mark
Factorisation using identities means rewriting an expression as a product by matching it with a known algebraic identity.
- 2
Add for 2 marks
Example: 9a2-25 = (3a)2-52 = (3a-5)(3a+5).
- 3
Add for 3 marks
Many expressions look difficult until the pattern is recognised.
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