(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
(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
(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
(9) Simplify:
(i) (2a + 3b + 4c)(4a2 + 9b2 + 16c2 - 6ab - 12bc - 8ca)
(ii) (x −2y + 3z)(x2 + 4y2 + 9z2 + 2xy + 6yz −3xz)
(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
(12) If 2x + (2/x) = 3, what is the value of x2 + 1/x2 ?
(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 ?
(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
(23) Factorize 4x² + 12xy + 9y²
(24) Factorize 16a² - 8a + 1
(25) Factorize 16a² - 9b²
(26) Factorize (a + b)² - (a - b)²
(27) Factorize 8x³ - 125y³
(28) Factorize 27x³ + 64y³
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