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Unit cube Activity 1 by Ms. Rashmi Kathuria
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Unit cube Activity 1 by Ms. Rashmi Kathuria

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This is an activity to verify the cubic algebraic formula for …

This is an activity to verify the cubic algebraic formula for
(a+b)^3..

Published in: Education, Technology

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  • 1. Algebraic Identities A presentation by.. Rashmi Kathuria
  • 2. Activity
    • Aim : To prove the algebraic identity
    • (a+b) 3 = a 3 +3a 2 b+3ab 2 +b 3
    • using unit cubes.
    • Material required: Unit Cubes.
  • 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. Observe the following
    • The number of unit cubes in a 3 = ..27…..
    • The number of unit cubes in 3a 2 b =…27…
    • The number of unit cubes in 3ab 2 =…9……
    • The number of unit cubes in b 3 =…1……
    • The number of unit cubes in a 3 + 3a 2 b + 3ab 2 + b 3
    • = ..64….
    • The number of unit cubes in (a+b) 3 =…64…
  • 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