OPERATIONS WITH FACTORIALS

Problem 1 :

3! + 2! = 

Solution:

3! + 2! = (3 × 2!) + 2!

2! in common, so will get

= 2! (3 + 1)

= (2 × 1) (4)

 = 8

Problem 2 :

3! + 6! = 

Solution:

3! + 6! = 3! + (6 × 5 × 4 × 3!)

3! in common, so will get

= 3! (1 + 120)

= 3! (121)

= 6 × 121

= 726

Problem 3 :

(3!)² = 

Solution:

(3!)² = (3 × 2 × 1)²

= 6²

= 36

Problem 4 :

5! + 4! = 

Solution:

5! + 4! = (5 × 4!) + 4!

4! in common, so will get

= 4! (5 + 1)

= 24 × 6

= 144

Problem 5 :

4! - 5! + 4 =       

Solution:

4! - 5! + 4 = 4! - (5 × 4!) + 4

4! in common, so will get

= 4! (1 - 5) + 4

= 24 (-4) + 4

= -96 + 4

= -92

Problem 6 :

2! × 5 - 12 = 

Solution:

= 2! × 5 - 12

= (2 × 1) × 5 - 12

= (2 × 5) - 12

= 10 - 12

= -2

Problem 7 :

(2! + 1!)³ = 

Solution:

(2! + 1!)³ = ((2 × 1!) + 1!)³

1! in common, so will get

= 1! (2 + 1)³

= 3³

= 27

Problem 8 :

(3! + 0!)³ = 

Solution:

= (3! + 0!)³

= (6 + 1)³

= 7³

= 343

Problem 9 :

(2! 0!)⁴ - 1 = 

Solution:

= (2! 0!)⁴ - 1 

= (2 × 1)⁴ - 1

= 2⁴ - 1

= 16 - 1

= 15

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