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Using unit cubes 3

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

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Using unit cubes 3

  1. 1. Algebraic Identities A presentation by.. Rashmi Kathuria
  2. 2. Activity <ul><li>Aim : To prove the algebraic identity </li></ul><ul><li>(a+b) 3 = a 3 +3a 2 b+3ab 2 +b 3 </li></ul><ul><li>using unit cubes. </li></ul><ul><li>Material required: Unit Cubes. </li></ul>
  3. 3. Start Working.. Take any suitable value for a and b. Let a=3 and b=1
  4. 4. Step 1. To represent a 3 make a cube of dimension a x a x a i.e. 3x3x3 cubic units.
  5. 5. Step 2. To represent 3a 2 b make 3 cuboids of dimension a x a x b i.e. 3x3x1 cubic units.
  6. 6. Step 3. To represent 3ab 2 make 3 cuboids of dimension a x b x b i.e. 3x1x1 cubic units.
  7. 7. Step 4. To represent b 3 make a cube of dimension a x a x a i.e. 1x1x1 cubic units.
  8. 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. 9. Observe the following <ul><li>The number of unit cubes in a 3 = ..27….. </li></ul><ul><li>The number of unit cubes in 3a 2 b =…27… </li></ul><ul><li>The number of unit cubes in 3ab 2 =…9…… </li></ul><ul><li>The number of unit cubes in b 3 =…1…… </li></ul><ul><li>The number of unit cubes in a 3 + 3a 2 b + 3ab 2 + b 3 </li></ul><ul><li>= ..64…. </li></ul><ul><li>The number of unit cubes in (a+b) 3 =…64… </li></ul>
  10. 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

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