PRACTICE QUESTIONS FOR a PLUS b WHOLE CUBE

(a+b)3  =  a3+3a2b+3ab2+b3

Problem 1 :

Expand (3x + 2y)

(A)  27x³ + 9 x² y + 4 x y² + 8 y³

(B)  27x³ + 54 x² y + 16 xy² + 8 y³

(C)  9x2 + 24 xy + 9y²

Problem 2 :

Expand (2a + b)³

(A) 8a³ + 12 a² b + 6a b² + b ³

(B) 27a³ + 27 a² b + 16 ab² + b³

(C) 25a² + 24 a²b + 12 ab² + 9b²

Problem 3 :

Expand (S + T) ³

 (A)  S³ - 3 S² T + 3 ST ² + T ³

 (B)  S³ - 3 S² T - 3 S T ² + T ³

 (C)  S³ + 3 S² T + 3 S T ² + T ³

Problem 4 :

Expand (3V + Q) ³

 (A) 27 V ³ + 2 V ² Q + 3 V Q² + Q³

 (B) 27V³ - 2 V ² Q - 3 V Q² + Q³

 (C) 27 V³ - 2 V²Q - 3V Q² + Q³

Problem 5 :

Expand (4T + 3Q) ³

(A)  64T³ - 96 T² Q - 108 T Q² + Q³

(B)  64T³ - 96 T² Q + 108 T Q² - Q³

(C)  64T³ + 96 T²Q + 108 T Q² + 27Q³

Problem 6 :

Expand (p + 5q)3

(A)  p³ - 15 p² q + 75 p q² - 125 q³

(B)  p³ - 15 p² q + 75 p q² + 125 q³

(C) p³ + 15 p² q + 75 p q² + 125 q³

Solutions for Practice Questions

Problem 1 :

Expand (3x + 2y)

Solution :

Here a  =  3x and b  =  2y

(3x + 2y)3  =  (3x)3 + 3(3x)2(2y) + 3(3x)(2y)2 + (2y)3

  =  33x3 + 3 (9x 2) (2y) + 3 (3x) (4y2) + 8y3

  =  27 x3 + 54 x 2y + 36 y2 + 8y3

Problem 2 :

Expand (2a + b)³

Solution :

Here a = 2a and b = b

(2a + b)3  =  (2a)3 + 3 (2a) 2 (b) + 3 (2a) (b)2 + (b)3

  =  23(a3) + 3 (4a) (b) + 3 (2a) (b)2 + (b)3

  =  8a3 + 12 a b + 6 a b2 + b3

Problem 3 :

Expand (S + T)3

Solution :

Here a  =  S and b  =  T

(S + T)3  =  S3 + 3 S2 T + 3 ST2 + T3

Problem 4 :

Expand (3V + Q)³

Solution : 

Here a  =  3V and b  =  Q

(3V + Q)3   =  (3V)3 + 3 (3V) 2 (Q) + 3 (3V) (Q)2 + (Q)3

  =  33V3 + 3(9V2)(Q) + 3 (3V) (Q)2 + (Q)3

  =  27V3 + 27 V 2Q + 9 VQ2 + Q3

Problem 5 :

Expand (4T + 3Q) ³

Solution :

here a  =  4T and b  =  3Q

(4T + 3Q)3  =  (4T)3 + 3(4T)2 (3Q) + 3(4T)(3Q)2 + (3Q)3

  =  43T3 + 3 (16 T 2) (3Q) + 3 (4T) (9Q2) + 33Q3

  = 64 T3 + 144 T 2 Q + 108 2 + 27 Q3

Problem 6 :

Expand (p + 5q)3

Solution :

here a  =  p and b  =  5q

(p + 5q)3  =  p3 + 3p2 (5q) + 3p(5q)2 + (5q)3

  = p3 + 3 p2 (5q) + 3 p (25q2) + (53q3)

  =  p3 + 15 p 2 q + 75 p q2) + 125q3

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