## Thursday, 2 June 2011

### Algebraic Identity test paper for class 8

8th   Algebraic Identity
Q. 1.    Find products using suitable algebraic Identity
(i)  (  x – 2/3 ) ( x+ 1/2  )
(ii)  (x  + 1/x   ) (  x4  + 1/x4 )
(iii) ( -3 x + 8 ) ( 2 + 7 x )
(iv) 87 x  92
(v) 234  x  229
Q. 2.  Expand each of the following
(i)  (3/2xy – 5/4 y2 z – xyz)2
(ii)  [ ( 2a-3b)2 ]2
(iii) (x2y – 2xy2+5yz2)2
(iv)  [ (2m2/n  - 3/r2 )2]2
(v)        [(2a-3b)2]2
Q. 3. Simplify
(i) (a + b + c)2 + (a  -  b + c)2   (ii) (a - b - c)2 - (a + b - c)2
(iii) (1/2 l – 2/3 m  - 1/5n)2 - ( 1/2 l +2/3 m -1/5n)2
Q.4. If a - b – c = 4 and –a b + b c – c a = -3             Find a 2 + b 2 + c 2
Q.5. If a2 + b 2 + c2  = 9 and b c+ ca + a b = 8          find ( a + b + c )2
Q6. x + y + z = 2 and x y + y z + z x = 1 find (x +y)2 + ( y + z )2 + ( z + x )2
Q. 7. Expand
(i) ( - 4p +5q)3
(ii) ( - 2 l – 3 m ) 3
Q. 8. Find value (i) 8x3 + 125 y3 If 2x + 5y = 7 and xy = 9
Q. 9. If 3p – 5q = 4 and 27 p3 -125 q3 = 8 Find pq
Q. 10. If ( a + 1/a )2 = 3 Prove a3 + 1/a3 = 0
Q.11. ( x + 2) +  = 5 find ( x + 2)3 +
Q.12. x + 1/x = P   show x3  + 1/x3 = p3 – 3p3
Q.13. y + 1/y = √3 prove y3 + 1/y3 =0
Q. 14.(a2 +1)/a = 4 Show (a6+1)/a3   = 52
Q.15. If p = 12 , q= 3 Find Value of p3 – 12p2q + 48pq2 – 64 q3

Algebraic Identity
(a + b)2 = a2 + b2+2ab
(a – b )2 = a2 + b2-2ab
(x + a) (x + b) = x2 +( a + b) x +a b
(a + b + c) 2  = a2  + b2 + c2+ 2ab + 2bc + 2ca
( a + b)3     = a3 + b3 +3 a2 b +3 a b2 = a3 + b3 +3 a b (a + b)
( a - b)3   =  a3 - b3  - 3 a 2b +3 a b2 = a3 + b3 -3 a b (a - b)