Long division methodDivide 3x3 – 5x2 + 10x – 3  by  3x + 1

FACTORISATION

COMMON MONOMIAL

COMMON BINOMIAL

BY GROUPING

DIFFERENCE OF 2 SQUARE

(a2- b2)=(a+b)(a-b)

PERFECT SQUARE

(a+b)2, (a-b)2

QUADRATIC TRINOMIALSSplitting the middle term (x2+px

+q)

X2+px+qX2+px+q ax2+bx+c

1)HCF (Highest Common Factor )They are of 2 types:a) Common monomial b) Common binomial

a)Common monomial Here we take out a common single term from 2 or more expressions b)Common binomial Here we take a common double term from 2 or more expressions and factorize it.

Example of common monomial and binomial

 a) 5x +20     = 5(x+4)        -example of common monomial

b)  3x2y-6xy2     =3xy(x-2)

a) 3(a-2b)2-5(a-2b) - example of common monomial=(a-2b) {3(a- 2b)- 5}  =(a-2b)(3a- 6b-5)

2)Factorization by perfect square • Here we identify the term as in the form as  (a+b)2 and  (a-b)2

 Example :-1)  9+6z+z2=      Z2+6z+9              =z2+32+2*x*3     =(z+3)2

2)a4+25b4-10a2b2

Let a2 = x;b2=yX2-10xy+25b2

=(x-5y)2=(a2-5b2)2

3) Factorization by quadratic trinomial

They are expressions written in the format of ax2+bx+c.So we split the middle term and factorize the expressions.Example:  2x2+9x+10= 2x2+5x+4x+10 =x(2x+5)+2(2x+5) =(2x+5)(x+2) 

Factorization by difference in squares

Here we identify the expressions in the form of :(a2 - b2)=(a + b)(a - b)Where we get the expressions either wayExample:(92 - 42)=(9 + 4)(9 - 4)= 81 – 36 + 36 – 16=81-16=65

Quiz1)Factorize :64 a2 + 80ab + 25b2

a)8a2 + 5b2 b) (8a +5b) 2 c) (8a - 5b) 2

2)Factorize :144a 2 – 169a) (12a + 13)(12a - 13 ) b)(12a + 13) 2

3)Factorize: a 4 - b 4

a)(a 2 - b 2 ) 2 b) (a 2 + b 2 ) 2 c)(a 2 + b 2)(a + b)(a - b)