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= ( 1 ) 1 3 3 2 3 3 6 32 1 y y y y y y y         = ( 1 ) ( 1 3 ) ( 1 ) 1 3 3 3          yy y y y y y y = ( 1 ) ...

If 2 1 2 1 ()   x x fx , find the value of 1 1 1 1 2 2 ̧ ¹ · ̈ © § ̧ ¹ ̈ · © § x f x f . If 2 1 2 4 () x x x gx   , sh ...

Chapter Three Algebraic Expressions Algebraic formulae are used to solve many algebraic problems. Moreover, many algebraic expre ...

Formula 1. (ab)^2 a^2  2 abb^2 Formula 2.(ab)^2 a^2  2 abb^2 Remark : It is seen from formula 1 and formula 2 that, adding ...

or, 2 2 4 ( ) 4 (a b) a b ab    Hence, 2 2 2 2 ̧ ̧ ¹ · ̈ ̈ © §  ̧ ̧  ¹ · ̈ ̈ © §  a b a b ab Remark : Product of any two q ...

= a^2 b^2 c^2  2 ab 2 bc 2 ac Example 1. What is the square of ( 4 x 5 y)? Solution :( 4 x 5 y)^2 ( 4 x)^2  2 u( 4 x)u( ...

Example 6. If xy 2 and xy 24 , what is the value of xy? Solution :(xy)^2 (xy)^2  4 xy ( 2 )^2  4 u 24 4  96 100 ? xy r 1 ...

Example 10. If abc 2 and abbcac 1 , what is the value of (ab)^2 (bc)^2 (ca)^2? Solution :(ab)^2 (bc)^2 (ca)^2 = a^ ...

(b)( 3 x 2 y)^2  2 ( 3 x 2 y)( 3 x 2 y)( 3 x 2 y)^2 (c)( 7 p 3 r 5 x)^2  2 ( 7 p 3 r 5 x)( 8 p 4 r 5 x)( 8 p 4 r ...

If a^4 a^2 b^2 b^4 8 and a^2 abb^2 4 , find the value of (i) a^2 b^2 ,(ii)ab. 3 ⋅3 Formulae of Cubes Formula 6.(ab)^3 a^3 ...

= (ab)(a^2  2 abb^2  3 ab) = (ab)(a^2 abb^2 ) Example 12. Find the cube of 2 x 3 y. Solution :( 2 x 3 y)^3 ( 2 x)^3  3 ...

Example 16. If a^2  3 a 1 0 , what is the value of^33 1 a a ? Solution : Given that, a^2  3 a 1 0 or,a^2  1 3 a or, 3 (^21 ...

Now, ̧ ¹ · ̈ ©  ˜ ˜ §  ̧ ¹ · ̈ ©  §  a a a a a a a a 1 1 3 1 1 3 3 3 =^23 ] 1 2 3 323 [ 3   a a = 2 3 3 2 3 3 3 ˜  u = ...

( 3 a 5 b)^3 ( 4 b 2 a)^3  3 (ab)( 3 a 5 b)( 4 b 2 a)? If ab m,a^2 b^2 n and a^3 b^3 p^3 , show that, m^3  2 p^3 3 m ...

(ii) 2 ab(xy) 2 bc(xy) 3 ca(xy) (xy)( 2 ab 2 bc 3 ca) (b) Expressing an expression in the form of a perfect square ; Exa ...

Example 6. Resolve into factors : x^2  5 x 6. Solution : x^2  5 x 6 x^2 ( 2  3 )x( 2 )( 3 ) = (x 2 )(x 3 ) Example 7 ...

Example 11. Resolve into factors : 8 x^3  36 x^2 y 54 xy^2  27 y^3. Solution : 8 x^3  36 x^2 y 54 xy^2  27 y^3 = ( 2 x)^3 ...

= ( 3 1 )( 9 3 1 ) 27 (^12) a a  a Here, in the second solution, the factors involving the variables are with integral coeffi ...

x^6 y^6 x^3 y^3  6 18. a^8 a^4  2 a^2 b^2  8 ab 105 20. x^2  37 a 650 4 x^4  25 x^2  36 22. 12 x^2  38 x 20 9 x^2 y ...

Now, if we indicate the dividend byf(x), the quotient by h(x), the remainder by r and the divisor by (xa), from the above formu ...