Mathematics

Factorisation

Factorisation is a Class 9 Mathematics topic within the chapter “Exploring Algebraic Identities.” Students learn how to rewrite algebraic expressions as products of simpler factors by taking out common factors, grouping terms, and applying identities such as the difference of squares and perfect-square forms. They practise recognising patterns, checking results by expansion, and using factorisation to simplify expressions and solve related algebraic problems accurately.

Hard · Level 5 · 1 questions

Practice questions

01Which is the correct factorisation of (a^2-b^2+2bc-c^2)?

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Answer and explanation

Correct answer: A. \((a-b+c)(a+b-c)\)

Write the expression as \(a^2-(b^2-2bc+c^2)\). Since \(b^2-2bc+c^2=(b-c)^2\), it becomes \(a^2-(b-c)^2\). Applying \(x^2-y^2=(x-y)(x+y)\) gives \((a-b+c)(a+b-c)\). Option B represents \(a^2-(b+c)^2\), which produces a negative \(2bc\) term. Exam tip: identify the perfect-square trinomial first and then use the difference-of-squares identity.

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Factorisation

Practice questions

01Which is the correct factorisation of (a^2-b^2+2bc-c^2)?(a^2-b^2+2bc-c^2) का सही गुणनखंड कौन सा है?

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01Which is the correct factorisation of (a^2-b^2+2bc-c^2)?