This is an introductory lesson on factorisation of algebraic expressions and explores some techniques involved
Introduction to CBSE Class 8 Mathematics Chapter "Factorisation"
“Factorisation” is a key chapter in the CBSE Class 8 Mathematics syllabus that delves into breaking down algebraic expressions into their simplest form. This chapter introduces students to the concept of factors of natural numbers, which are then extended to polynomial expressions. It begins with the factorisation of common terms and advances to techniques such as regrouping terms, splitting the middle term, and using identities to simplify and solve quadratic and cubic polynomial expressions.
The chapter aims to strengthen students’ understanding of how factorisation is applied to simplify algebraic expressions and solve equations efficiently. By mastering factorisation, students can solve a variety of problems, including those involving finding values of algebraic expressions for specific values of variables. Factorisation also plays a significant role in finding the LCM and GCD of polynomials, thereby linking arithmetic to algebra.
Assignments for CBSE Class 8 Mathematics Chapter “Factorisation”
- Factor Hunt: Factorise different algebraic expressions and identify their factors.
- Real-life Application: Describe a real-life situation where factorisation might be used and demonstrate how to apply it.
- Exploring Identities: Use algebraic identities to factorise given expressions and verify the results by expansion.
- Creative Factors: Craft a story problem that involves factorisation and present the solution.
- Puzzle Time: Create and solve a puzzle where the clues lead to factorisation of polynomials.
Conclusion The chapter “Factorisation” in CBSE Class 8 Mathematics serves as an essential building block for understanding algebraic expressions and equations. It equips students with a fundamental skill set that not only aids in simplifying and solving algebraic challenges but also lays the groundwork for future studies in mathematics and sciences.
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Questions and Answers for CBSE Class 8 Mathematics Chapter "Factorisation"
- Q1: What is factorisation?
ANS: Factorisation is the process of breaking down a complex expression into simpler factors that, when multiplied together, give the original expression. - Q2: Why is factorisation important in mathematics?
ANS: Factorisation is important because it simplifies expressions, making it easier to solve equations and understand algebraic structures. - Q3: What is a common factor in algebraic expressions?
ANS: A common factor is a term that is present in all terms of an expression, which can be factored out to simplify the expression. - Q4: How do you factorise a polynomial using the middle term splitting method?
ANS: To factorise a polynomial using the middle term splitting method, you split the middle term into two terms such that their product is equal to the product of the squared term coefficient and the constant term. - Q5: Can all algebraic expressions be factorised?
ANS: Most algebraic expressions can be factorised, but some cannot be broken down into simpler factors over the set of integers. - Q6: What role do algebraic identities play in factorisation?
ANS: Algebraic identities help in factorisation by providing standard forms that can be used to quickly factorise certain types of expressions. - Q7: How does factorisation help in finding the LCM and GCD of polynomials?
ANS: Factorisation allows us to break down polynomials into their prime factors, making it easier to identify the least common multiples (LCM) and greatest common divisors (GCD). - Q8: What is a factor tree, and how is it used in factorisation?
ANS: A factor tree is a diagram used to break down a number into its prime factors. It’s not commonly used for algebraic expressions but can help understand factorisation of numbers. - Q9: How do you check if your factorisation is correct?
ANS: You can check factorisation by multiplying the factors and verifying if the product is the original expression. - Q10: How can factorisation be used to solve quadratic equations?
ANS: Factorisation can be used to solve quadratic equations by setting the factored form of the equation to zero and solving for the variable, which gives the roots of the equation.
