PRACTICE TEST IN ALGEBRA

(1)  Expand following 

(i)  (2x + 3y + 4z)2

(ii) (−p +2q + 3r)2

(iii) (2p + 3)(2p −4)(2p −5)

(iv) (3a +1)(3a −2)(3a + 4)           Solution

(1)  Using algebraic identity, find the coefficients of x2 , x and constant term without actual expansion.

(i) (x + 5)(x + 6)(x + 7)

(ii) (2x + 3)(2x −5)(2x −6)            Solution

(2)  If (x + a)(x + b)(x + c) = x3 + 14x2 + 59x + 70 , find the value of

(i)  a + b + c

(ii)  (1/a) + (1/b) + (1/c)

(iii)  a2 + b2 + c2

(iv)  (a/bc) + (b/ac) + (c/ab)          Solution

(3)  Expand :

(i) (3a - 4b)3

(ii)  (x + (1/y))3                  Solution

(2)  Evaluate the following by using identities:

(i) 983

(ii)  10013                 Solution

(3)  If (x + y + z) = 9 and (xy + yz + zx) = 26, then find the value of x2 + y2 + z2                 Solution

(4)  Find 27a3 + 64b3 , if 3a + 4b = 10 and ab = 2

Solution

(5)  Find x3 - y3, if  x - y  =  5 and xy  =  14   Solution

(6)  If a + (1/a)  =  6, then find the value of a3 + 1/a3

Solution

(7)  If x2 + 1/x2  =  23, then find the value of

x + (1/x) and x3 + (1/x3)         

 Solution

(8)  If (y - (1/y))3  =  27, then find the value of

y3 - (1/y)3

Solution

(9)  Simplify: 

(i)  (2a + 3b + 4c)(4a2 + 9b2 + 16c2 - 6ab - 12bc - 8ca)

(ii) (x −2y + 3z)(x2 + 4y2 + 9z2 + 2xy + 6yz −3xz)

Solution

(10)  By using identity evaluate the following:

(i) 73 - 103 + 33

(ii)  1 + (1/8) - (27/8)            Solution

(11)  If 2x −3y −4z = 0 , then find 8x3 - 27y3 - 64z3

Solution

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