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Algebraic Identities A presentation by.. Rashmi Kathuria
Activity ,[object Object],[object Object],[object Object],[object Object]
Start Working.. Take any suitable value for  a  and b. Let a=3  and b=1
Step 1.   To represent a 3  make a cube of dimension  a x a x a i.e. 3x3x3 cubic units.
Step 2.  To represent 3a 2 b  make 3 cuboids of dimension a x a x b i.e. 3x3x1 cubic units.
Step 3. To represent 3ab 2   make 3 cuboids of dimension a x b x b i.e. 3x1x1 cubic units.
Step 4. To represent b 3  make a cube of dimension  a x a x a i.e. 1x1x1 cubic units.
Step 5. Join all the cubes and cuboids formed in the previous steps to make a cube of  dimension  (a +b) x ( a +b) x ( a +b)  i.e. 4x4x4 cubic units. = + + +
Observe the following ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
It is observed that the number of unit cubes  in (a+b) 3  is equal to the number of unit cubes in a 3  +3a 2 b+3ab 2 +b 3  . Learning outcome

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Using unit cubes 3

  • 1. Algebraic Identities A presentation by.. Rashmi Kathuria
  • 2.
  • 3. Start Working.. Take any suitable value for a and b. Let a=3 and b=1
  • 4. Step 1. To represent a 3 make a cube of dimension a x a x a i.e. 3x3x3 cubic units.
  • 5. Step 2. To represent 3a 2 b make 3 cuboids of dimension a x a x b i.e. 3x3x1 cubic units.
  • 6. Step 3. To represent 3ab 2 make 3 cuboids of dimension a x b x b i.e. 3x1x1 cubic units.
  • 7. Step 4. To represent b 3 make a cube of dimension a x a x a i.e. 1x1x1 cubic units.
  • 8. Step 5. Join all the cubes and cuboids formed in the previous steps to make a cube of dimension (a +b) x ( a +b) x ( a +b) i.e. 4x4x4 cubic units. = + + +
  • 9.
  • 10. It is observed that the number of unit cubes in (a+b) 3 is equal to the number of unit cubes in a 3 +3a 2 b+3ab 2 +b 3 . Learning outcome