Class 8 Chapter 7: Factorization

# 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)

·

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

·

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)

·

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!

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