Class 8 Chapter 7: Factorization

Important Concepts and Formulas

1.      Factorizing an algebraic expression means expressing it as a product of various factors till they are irreducible.

2.      We use the following methods for factorizing algebraic expressions:

            ·        Bytaking out common factors:

             For example, 15a + 20b = 5(3a) + 5(4b) = 5(3a + 4b)

            ·        Groupingthe terms:

              For example, 49a + 42c – 7ay – 6cy = (49a – 7ay) + (42c – 6cy)
                                                                        = 7a(7 – y) + 6c(7 – y)
                                                                        = (7 – y) (7a + 6c)

            ·        Factorizingquadratic trinomials:

             For example, x² + 7x + 12 = x² + (4 + 3)x + 4 ­× 3

                                                                      = x² + 4x + 3x + 12  

                                                         = x(x + 4) + 3(x + 4)

                                                         = (x + 4)(x + 3)      

           ·        Factorizationby using identities:

                    I.       Factorization using a² + 2ab + b² = (a + b)²

For example, x² + 18x + 81 = x² + 2(x)(9) + 9² = (x + 9)²

                  II.      Factorization using a² + 2ab + b² = (a + b)²

For example, 4x² – 20xy + 25y² = (2x)² – 2(2x)(5y) + (5y)² = (2x – 5y)²

                III.      Factorization using a² – b² = (a + b) (a – b)

                 For example, 9x² – 16y² = (3x)² – (4y)² = (3x + 4y) (3x – 4y)  

                   To study the above methods in detail -------- Click Here!