PRACTICE TEST USING ALGEBRAIC IDENTITIES

(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

(12)  If 2x + (2/x)  =  3, what is the value of x² + 1/x² ?

Solution

(13)  If a+b+c  =  6 and a²+b²+c²  =  14, what is the value of (a-b)² + (b-c)² + (c-a)² ?        Solution

(14)  If x-y  =  8 and xy  =  5, what is the value of

x³-y³+8(x+y)²    Solution

(15)  If x + y  =  5 and xy  =  6 and x > y, then find 2(x²+y²)          Solution

(16)  If a³-b³  =  513 and a-b  =  3, what is the value of ab ?             Solution

(17)  If a²+b²+c²  =  9 and ab+bc+ca  =  8, what is the vale of (a+b+c)²         Solution

(18)  a+b  =  √7 and a-b  =  √5, then find the value of 8ab(a²+b²)           Solution

(19) If a-b  =  4 and ab  =  60, what is the value of a+b ?

Solution

(20)  If a+b  =  9m and ab  =  18m², what is the value of a-b ?  Solution

(21)  Simplify :

(2345 x 2345 - 759x759)/(2345-759)

(22)  Factorize 9x² - 24xy + 16y²

Solution

(23)  Factorize 4x² + 12xy + 9y²

Solution

(24)  Factorize 16a² - 8a + 1

Solution 

(25)  Factorize 16a² - 9b²

Solution

(26)  Factorize (a + b)² - (a - b)²

Solution

(27)  Factorize 8x³ - 125y³

Solution

(28)  Factorize 27x³ + 64y³

Solution

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