PRACTICE QUESTIONS FOR a CUBE MINUS b CUBE

a3-b3= (a+b) (a2-ab+b2)

Problem 1 :

Expand (2x)3 - y3

(A) (2x-y) (4x²+2xy+y²)

(B) (2x+y) (4x²+2xy+y²)

(C)  (x-y) (4x²-xy+y²)

Problem 2 :

Expand x³ - (3y)³

(A) (x+3y) (4x²+3xy-9y²)

 (B) (x+3y) (x²-3xy+9y²)

 (C) (x-3y) (x²+3xy+9y²)

Problem 3 :

Expand (3x)³ - y³

(A) (3x-y) (9x²+3xy+y²)

(B) (3x-y) (9x²+3xy-y²)

(C) (3x+y) (9x²-3xy-y²)

Problem 4 :

Expand (2S)³ - T³

(A)  (2S-T) (4S2+2ST+T²)

(B)  (2S+T) (8S2+2ST+T²)

(C)  (2S-T) (4S²-2ST+T²)

Problem 5 :

Expand (3N)³ - (2L)³

(A) (3N-2L) (9N²+6NL+4L²)

(B)  (3N+2L) (9N²-6NL-4L2)

(C) (3N-2L) (9N²-6NL+4L²)

Problem 6 :

Expand p³-q³

(A) (p-q) (p²-pq-q²)

(B) (p-q) (p²+pq+q²)

(C) (p+q) (p²+pq+q²)

Solutions for Practice Questions

Problem 1 :

Expand (2x)3 - y3

Solution :

Here a = 2x and b = y

(2x)3 - y3  =  (2x-y)[(2x)2+2xy+y2]

  =  (2x-y)(4x2+2xy+y2)

Problem 2 :

Expand x³ - (3y)³

Solution :

here a = x and b = 3 y

x3-(3y)3 = (x-3y)(x2+x(3y)+(3y)2)

  = (x-3y)[x2+3xy+(32y2)]

  = (x-3y)(x2 + 3 x y + 9y2)

Problem 3 :

Expand (3x)³ - y³

Solution :

here a  =  3x and b  =  y

(3x)3-y3 = (3x-y)(x2+3xy+y2)

  = (3x-y)(x2 + 3xy+y2)

Problem 4 :

Expand (2S)³ - T³

Solution :

here a  =  2S and b  =  T

(2S)3 - T3  =  (2S-T)[(2S)2+(2S)T+T2]

                    = (2S-T)(4S2+2ST+T2)

Problem 5 :

Expand (3N)³ - (2L)³

Solution :

here a = 3 N and b = 2 L

(3N)3-(2L)3  =  (3N-2L)[(3N)2+(3N)(2L)+(2L)2]

  =  (3N-2L)(9N2+6NL+4L2)

Problem 6 :

Expand p³-q³

Solution :

Here a  =  p and b  =  q

P3-q3  =  (p-q)(p2+pq+q2)

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