Factorisation Class 8 Notes- Chapter 14

What are Factors?

An expression can be factorised into the product of its factors. These factors can be algebraic expressions, variables and numbers also.

Irreducible factors

When an expression cannot be further factorized as a product of factors, then it is termed as irreducible factors.

Common Factor Method

An expression can be factorised in a systematic manner through this method. Some steps in this method are:

  1. Each term of an expression can be written as the product of irreducible factors.
  2. Identify and distinguish the common factors.
  3. With respect to the distributive law, combine the remaining factors.

Regrouping

This stands for rearrangement of terms. In an expression, if all the terms don’t have any common factors then we can group the terms in such manner in which each group can have a common factor which will help in factorising the expression. The regrouping method may not result in factorisation all the time, but we must be observant in trial and error and come up with the desired regrouping.

All the expressions can be put in the form

\(a^{2}+2ab+b^{2},a^{2}-2ab+b^{2},a^{2}-b^{2} and x^{2}+(a+b)+ab\)

Facorisation of these epressions can be shown below as:

\(a^{2}+2ab+b^{2}=(a+b)^{2}\) \(a^{2}-2ab+b^{2}=(a-b)^{2}\) \(a^{2}-b^{2}=(a+b)(a-b)\) \(x^{2}+(a+b)x+ab=(x+a)(x+b)\)

Same as numerical, we can use the functionality of division which is the inverse of multiplication in solving algebraic expressions.

Important Questions

  1. Solve the following equations \(3x^{2}+1/3x^{2}=1+1=2\)
  2. Factorise and divide the following \(8(x^{3}y^{2}z^{2}+x^{2}y^{3}z^{2}+x^{2}y^{2}z^{3})\div 4x^{2}y^{2}z^{2}\)
  3. Do the following divisions \(12a^{8}b^{8}\div (-6a^{6}b^{4})\)
  4. Factorise the given \((l+m)^{2}-4lm\)
  5. Find out the common factors, \(3x^{2}y^{3},10x^{3}y^{2},6x^{2}y^{2}z\)

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Practise This Question

Which is the greatest 5 digit perfect square number?