CBSE Class 8 Math, Factorization

•   Factorisation means write an expression as a product of' its factors.

•   Like prime factors, an irreducible factor, a factor which cannot be expressed further as a product of factors.

•   Some expression can easily be factorised using these identities:

      I. a² + 2ab + b² = (a + b)²

      II. a² – 2ab + b² = (a – b)²

      III. a² – b² = (a – b)(a + b)

      IV. x² + (a + b)x + ab = (x + a)(x + b)

•   The number 1 is a factor of every algebraic term also, but it is shown only when needed.

•   When factorisation of x² + (a + b)x + ab is done by splitting the middle term, the two numbers which give the product ab and (a + b) as the coefficient of x have to be chosen very caully with correct sign.

      (i) a² + 2ab + b² = (a + b)²

      (ii) a² – 2ab + b² = (a – b)²

      (iii) a² – b² = (a – b)(a + b)

      (iv) 1 is a factor of every term of an algebraic expressionless it is specially required, we do not show I as a separate factor of any term.

      (v) Factorisation means writing an expression as product Of factors.

Note: In case of factorisation of a term of an expression, the word 'irreducible' is used in place of 'prime'.

      For example, 6pq = 2 × 3 × pq is not the irreducible corm because pq can further be factorised as p × q, i.e. the irreducible fonn of 6pq = 2 × 3 × p × q.

Example: Write 10xy as irreducible factor form.

Solution: We have          10 = 2 × 5

                                                   xy = x × y

                                                   10xy = 2 × 5 × x × y