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Question
Mathematics
  1. 11 x 2 165 x 11x^(2)-165 x
  2. 4 n a 2 20 n a b 4na^(2)-20 nab
45 h 3 k 20 h 2 k 2 + 100 h k 45h^(3)k-20h^(2)k^(2)+100 hk
5 3 p 4 + 15 p 2 + 6 p 5*3*p^(4)+15p^(2)+6p
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  1. Answer: 11 x 2 165 x = 11 x ( x 15 ) 11x^(2)-165 x=11 x(x-15).
    Step-by-step solution:
  • Take out the common factor, 11x:
    11 x ( x 15 ) 11 x(x-15).
  1. Answer: 4 n a 2 20 n a b = 4 n a ( a b ) 4na^(2)-20 nab=4na(a-b).
    Step-by-step solution:
  • Take out the common factor, 4 n a 4na:
    4 n a ( a b ) 4na(a-b).
  • Simplify the expression by factoring out ( a b ) (a-b):
    4 n a ( a b ) 4na(a-b).
  1. Answer: 45 h 3 k 20 h 2 k 2 + 100 h k = 5 h k ( 9 h 2 4 h k + 20 ) 45h^(3)k-20h^(2)k^(2)+100 hk=5hk(9h^(2)-4hk+20).
    Step-by-step solution:
  • Take out the common factor, 5 h k 5hk:
    5 h k ( 9 h 2 4 h k + 20 ) 5hk(9h^(2)-4hk+20).
  • There are no further simplifications, so we stop here.
  1. Answer: 5 3 p 4 + 15 p 2 + 6 p = 15 p ( p 4 + 1 ) + 6 p 5*3*p^(4)+15p^(2)+6p=15 p(p^(4)+1)+6p.
    Step-by-step solution:
  • Take out the common factor, 3 p 3p:
    3 p ( 5 p 4 + 5 p 2 + 2 ) 3p(5p^(4)+5p^(2)+2).
  • Simplify the expression inside the parentheses by factoring out p 2 p^(2):
    3 p ( 5 p 2 ( p 2 + 1 ) + 2 ) 3p(5p^(2)(p^(2)+1)+2).
  • Simplify again by factoring out p 2 + 1 p^(2)+1:
    3 p ( p 2 + 1 ) ( 5 p 2 + 2 ) 3p(p^(2)+1)(5p^(2)+2).
  • There are no further simplifications, so we stop here.
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