PRACTICE QUESTIONS FOR a MINUS b WHOLE CUBE

(a-b)3  =  a3-3a2b+3ab2-b3

Problem 1 :

Expand (x - 2y)3

 (A)  x³ + 6 x² y - 6 xy² + 8 y³

 (B)  x³ - 6 x² y + 12 xy² - 8 y³

 (C)  2x³ + 6 x² y + 6 xy² + 8 y³

Problem 2 :

Expand (2a - b)³

 (A)  8a³ - 12 a² b + 6a b² - b3

 (B)  8a³ + 12 a² b + 6a b² + b³

 (C)  8a³ + 12 a² b + 6a b² - b³

Problem 3 :

Expand (3S - T)³

 (A)  27S³ - 27 S²T + 9 ST ² - T³

 (B)  8S³ + 24 S²T + 2S T ² + T³

 (C)  S³ + 9S²T - 64 S T ² + T³

Problem 4 :

Expand (V - 5Q)3

 (A) V ³ -15 V ² Q + 75 V Q² - 125 Q³

 (B) 27 V ³ - 2 V ² Q + 3 V Q² - Q³

 (C) 27 V ³ - 2 V ² Q + 3 V Q² - Q³

Problem 5 :

Expand (4T - Q)³

 (A) 64T³ - 96 T² Q - 108 T Q² + Q ³

 (B) 64T³ - 96 T² Q + 108 T Q² - Q ³

 (C) 64T³ - 48 T² Q + 12 T Q² + Q³

Problem 6 :

Expand (5p - q)³

(A)  p3 - 15 p²q + 75 pq² - 125 q³

(B)  p³ - 15 p²q + 75 p q² + 125 q³

(C) 125 p³ - 75 p²q + 15 p q² + q³

Solutions for Practice Questions

Problem 1 :

Expand (x - 2y)3

Solution :

Here a  =  x and b  =  2y

(x-2y)2  =  x2 - 3 x2 (2y) + 3 x (2y)2 - (2y)3

  =  x2 - 6 x2 y + 3 x (22y2) - (23y3)

  =  x2 - 6 x2 y + 12 x y2 - 8 y3

Problem 2 :

Expand (2a - b)³

Solution :

Here a  =  2a and b  =  b

(2a-b)3  =  (2a)3 - 3 (2a)2 (b) + 3 (2a)b2 - b3

  =  (23a3) - 3 (22a2) (b) + 3 (2a)(b)2 - (b)3

  =  8a3 - 12 a2b + 6 ab2 - b3

Problem 3 :

Expand (3S - T)³

Solution :

here a = 3S and b = T

(3S-T)3  =  (3S)3 - 3(3S)2 T + 3(3S)T2 - T3

  =  (33S3) - 3 (32S2)T + 3 (3S)T2 - T3

  =  27S3 - 3 (9S2)T + 3 (3S)T2 - T3

  =  27S3 - 27S2T + 9 S T2 - T3

Problem 4 :

Expand (V - 5Q)3

Solution :

Here a  =  V and b  =  5Q

(V - 5Q)3  =  V3 - 3 V2 (5Q) + 3 V(5Q)2 - (5Q)3

= V3 - 3 V2 (5Q) + 15 VQ2 - (53Q3)

= V3 - 15 V2 Q + 15 V Q2 - 125 Q3

Problem 5 :

Expand (4T - Q)³

Solution :

Here a  =  4T and b  =  Q

(4T-Q)3  =   (4T)3 - 3 (4T)2 (Q) + 3 (4T)(Q)2 - Q3

  =  (43T3) - 3 (42T2)(Q) + 3 (4T)Q2 - Q3

  =  64 T3 - 3 (16 T2)(Q) + 12 T Q2 - Q3

 = 64 T3 - 48 T2Q + 12 T Q2 - Q3

Problem 6 :

Expand (5p - q)³

Solution :

Here a = 5p and b = q

(5p - q)3 = (5p)3 - 3 (5p)2 (q) + 3 (5p)(q)2 - (q)3

  =  (53p3) - 3 (52p2) (q) + 15 p q2 - q3

   = 125 p3 - 75 p2q + 15 p q2 - q3

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