untitled

( 3 a 5 b)^3 ( 4 b 2 a)^3  3 (ab)( 3 a 5 b)( 4 b 2 a)?

8. If ab m,a^2 b^2 n and a^3 b^3 p^3 , show that, m^3  2 p^3 3 mn.


9. If`xy 1 , show that, x^3 y^3 xy (xy)^2


10. If ab 3 and ab 2 , find the value of (a) a^2 abb^2 and (b) a^3 b^3.


11. If ab 5 and ab 36 , find the value of (a) a^2 abb^2 and (b) a^3 b^3.


12. If a
    m

m

1

, find the value of^33

1

m

m.

13. If p
    x

x

1

, find the value of^33

1

x

x .

14. If 1
    1
    
    a

a , show that, 4.

1

3

(^3) 
a
a

15. If abc 0 , show that,

(a)a^3 b^3 c^3 3 abc (b) 1

3

( )

3

( )

3

( )^222











ab

a b

ca

c a

bc

b c

.

16. If pq r, show that, p^3 q^3 r^3 3 pqr


17. If 3

2

2 

x

x , show that, 63

1

8 3 3 ̧

¹

·

̈

©

§



x

x.

18. If a 6  5 , find the value of 3

(^61)
a
a 
.

19. If 18 3
    1
    3

(^3) 
x
x , prove that, x^3 ^2.

20. If a^4 a^2  1 0 , prove that, 0
    1
    3

(^3) 
a
a.
3 ⋅4 Resolution into Factors
If an expression is equal to the product of two or more expressions, each of the latter
expressions is called a factor of the former expression.
After finding the possible factors of any algebraic expression and then expressing the
expression as the product of these factors are called factorization or resolution into
factors.
The algebraic expressions may consist of one or more terms. So, the factors may also
contain one or more terms.
Some process of resolving expressions into factors :
(a) If any polynomial expression has common factor in every term, at first
they are to be found out. For example,
(i) 3 a^2 b 6 ab^2  12 a^2 b^2 3 ab(a 2 b 4 ab)