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**Algebraic Expressions**

and Identities

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**Identities to be remembered:**

(a + b)2 = a2 + b2 +2ab (a - b)2 = a2 + b2 - 2ab (x + a)(x + b) = x2 + (a + b)x + ab (a - b)(a + b) = a2 – b2 (a+b)3 = a3 +b3 + 3ab(a+b) =a3 + 3a2b+3ab2 + b3 (a-b)3 = a3 - b3 - 3ab(a - b) =a3 - 3a2b +3ab2 - b3

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The value of : (67.542) (32.458)2 100 Choose the correct option: b)10 a) 1 d)20 c)100

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**Find the missing term in the following equation:**

? (2x+ 3) (2x+ 4) = 4x Choose the correct option: a) 7x b) 14x 14x Ans: c) 6x d) 8x

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**Fill in with he missing term:**

(-15x) (5x + 4)(5x – 7) = 25x = 25x x Choose the correct option: a) 15x b) 55x c) -3x d) -15x

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**Fill in with the missing term:**

27a (-3a - 7)(-3a – 2) = 9a Choose the correct option: a) 27a c) -27a b) 15a d) -15a

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**Fill in with the missing term:**

(-8a) (-2a + 8)(-2a – 4) = 4a = 4a - 8a Choose the correct option: a) -8a c) 8a b) 4a d) 16a

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**Fill in with the missing term:**

70pq (5p + 7q)2 = 25p q2 (-2a + 5b)2 = 4a b2 = 4a b2 ( -3f - 8g)2 = 9f g2 (-20ab) ab 48fg

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**Find the missing term in the following equation:**

? Choose the correct option: a) 2xy b) -2xy a) 2xy ANS: c) 12xy d) -12xy

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**= + + ab (-xy) - xy Fill in with the missing term: a) ab b) = +**

= ab (-xy) - xy

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**(-pq) - pq Fill in with the missing term: = +**

= (-pq) - pq

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If 6x – 4y = 3 , xy = 2 , then : 36x2 + 16y2 = 105

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If (-15p – 4q) = -3 , pq = -1, then : 225p2 + 16q2 = 129

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If (3a + 5b) = - 4 , 9a2 + 25b2 = -14 , then : ab= 01(one)

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If 9m2 + 49n2 = -3 , mn = 2 , then: 3m + 7n = 09

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If 25a2 + 81b2 = 216 , ab = -4 , then: 5a – 9b = 24

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If 4a b2 = 48 , ab = -2 , then: a – 6b = 06

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If 25x y2 = -90 , and 5x + 8y =10 , then : 5x – 8y = -9

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**02 If 256x2 - 81y2 = 72, 16x - 9y = 12p and 16x + 9y = 3q , then :**

pq = 02

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If , then : 79

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If , then : 38

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If , then : 12

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If , then : 20

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If , then : 15

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If , then : 23

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**Expand : (3a + 2b)3 = (4x + 7y)3 = ................ 27a3 + 54a2b**

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**Expand : (8y – 5x )3 = (3b – 7a)3 = 512y3 - 960y2x + 600x2y - 125x3**

512y3 y2x + 600x2y x3 27b3 b2a ba2 a3

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**Expand : (-2d + 7a)3 = (-a - 6c)3 = - 8d3 + 84d2a - 294da2 + 343a3**

- a3 - 18a2c - 108ac2 - 216c3

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