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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)