PRACTICE QUESTIONS FOR a PLUS b WHOLE CUBE

(a+b)³  =  a³+3a²b+3ab²+b³

Problem 1 :

Expand (3x + 2y)³ 

(A)  27x^³ + 9 x^² y + 4 x y^² + 8 y^³

(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

Expand :

Problem 7 :

(3a - 4b)³

Problem 8 :

(x + (1/y))³

Evaluate the following by using identities:

Problem 9 :

98³

Problem 10 :

1001³

Problem 11 :

If (x + y + z) = 9 and (xy + yz + zx) = 26, then find the value of x² + y² + z²

Problem 12 : 

Find 27a³ + 64b³ , if 3a + 4b = 10 and ab = 2

Solutions for Practice Questions

Problem 1 :

Expand (3x + 2y)³ 

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

Expand :

Problem 7 :

(3a - 4b)³

Solution :

a = 3a and b = 4b

(a - b)³ = a³ - 3a² b + 3ab² - b³

= (3a)³ - 3(3a)² (4b) + 3(3a)(4b)² - (4b)³

= 27a³ - 3(9a²) (4b) + 3(3a)(16b²) - (64b³)

= 27a³ - 108a²b + 144ab² - 64b³

Problem 8 :

(x + (1/y))³

Solution :

a = x and b = 1/y

(a + b)³ = a³ + 3a² b + 3ab² + b³

= x³ - 3x² (1/y) + 3x(1/y)² - (1/y)³

= x³ - (3x²/y) + (3x/y²) - (1/y³)

Evaluate the following by using identities:

Problem 9 :

98³

Solution :

(a - b)³ = a³ - 3a² b + 3ab² - b³

98 = 100 - 2

= (100)³ - 3(100)² (2) + 3(100)(2)² - 2³

= 1000000 - 3(10000) (2) + 3(100)(4) - 8

= 1000000 - 60000 + 1200 - 8

= 1001200 - 60008

= 941192

Problem 10 :

1001³ 

Solution :

(a + b)³ = a³ + 3a² b + 3ab² + b³

1001 = 1000 + 1

= (1000)³ + 3(1000)² (1) + 3(1000)(1)² + 1³

= 1000000000 + 3(1000000) + 3(1000) + 1

= 1003003001

Problem 11 :

If (x + y + z) = 9 and (xy + yz + zx) = 26, then find the value of x² + y² + z²  

Solution :

x² + y² + z²  = (x + y + z)² - 2(xy + yz + zx) 

Applying the given values, we get

x² + y² + z²  = 9² - 2(26) 

= 81 - 52

= 29

Problem 12 :

Find 27a³ + 64b³, if 3a + 4b = 10 and ab = 2

Solution :

a³ + b³ = (a + b)³ - 3ab(a + b)

(3a)³ + (4b)³ = (3a + 4b)³ - 3(3a)(4b)(3a+ 4b)

= (3a + 4b)³ - 36ab(3a+ 4b)

= 10³ - 36(2)(10)

= 1000 - 720

= 280

Related Topics

• Practice for (a+b)²
  
• Practice for (a-b)²
  
• Practice for (a-b)³
• Practice for (a³+ b³)
• Practice for (a³- b³)
• Practice for (a²- b²)
• Practice for (a + b + c)²
• Practice for (x + a)(x + b)
• Algebra Formulas
• Practical problems in algebra
• Algebra worksheets 
• 10th grade algebra worksheets
• More topics on algebra
• Algebraic identities 
• More calculators 
• Algebra practice test
  

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.