Factorization

The following methods are used for factorization.

1. taking common at the first time

The first method of factorization is taking common. Some Examples are mentioned below

a) 2a + 4b = 2a + 2x2b = 2 (a+2b) Here 2 is common.

b) 3xy + 6y = 3xy + 3x2y = 3y(x+2y) Here, 3y is common.

c) (a+b) (x+y) + (a-b) (a+b) = (a+b) {(x+y) + (a-b)} Here, (a+b) is common.

• Use formula method at the second method.

The following formula is most important useful for formula method.

a) (a+b)² = a² + 2ab + b²

b) (a-b)² = a² – 2ab + b² or, (a+b)²– 4ab

c) a²+b² = (a+b)²– 2ab or, (a-b)² + 2ab

d) a²– b² = (a+b) (a-b)

e) (a+b) ³ = a³+3a²b+3ab²+b³ or, a³+b³+ 3ab(a+b)

f) (a-b)³ = a³-3a²b +3ab²-b³ or, a³-b³ – 3ab(a-b)

g) a³+b³ = (a+b) (a²– ab + b²) or, (a+b)³ – 3ab(a+b)

h) a³ – b³ = (a-b) (a²+ab+b²) or, (a-b)³ + 3ab(a-b)

• 1st x last at the last method (if does not solved with first and second method.)

1. ) 3x²+7xy+4y²

      = 3x²+xy(3+4)+4y²

      = 3x²+3xy+4xy+4y²

      = 3x (x+y)+4y(x+y)

      = (x+y) (3x+4y) Ans.