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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