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Algebraic Identities… By RASHMI KATHURIA
Activity 4 <ul><li>Aim :  To prove the algebraic identity </li></ul><ul><li>a 3 +b 3  =(a+b)(a 2  -ab+b 2 )   </li></ul><u...
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.
Step2.  To represent  (b) 3   take a cube of dimension b x b x b i.e. 1x1x1  cubic units.
Step3.  To represent  a 3 +b 3   add a cube of dimension b x b x b i.e. 1x1x1 to  the cube formed in the step 1 of dimensi...
Step4. To represent  (a+b)a 2   make a cuboid of dimension (a +b) x a x a i.e. 4x3x3  cubic units.
Step5.  To represent  (a+b)a 2 +(a+b)b 2   add a cuboid of dimension (a +b) x b x b i. e 4 x1 x 1 to the cuboid formed in ...
Step6.  To represent  (a+b)a 2 +(a+b)b 2 -(a+b)ab  extract a cuboid of dimension  (a+b) x a x b  i.e. 4x3x1  cubic units f...
Step7. Rearrange the unit cubes left to form the shape formed in the  Step 3.
Observe the following <ul><li>The number of unit cubes in a 3  = …27….. </li></ul><ul><li>The number of unit cubes in b 3 ...
It is observed that the number of unit cubes  in a 3 +b 3  is equal to the number of unit cubes in (a+b)a 2  -(a+b)ab+(a+b...
Acknowledgement <ul><li>I would like to thank my sister  who has helped me to click these picture from the mobile and then...
Thank You
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Uising unit cubes 2

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This is an activity to verify the formula a^3-b^3.

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Transcript of "Uising unit cubes 2"

  1. 1. Algebraic Identities… By RASHMI KATHURIA
  2. 2. Activity 4 <ul><li>Aim : To prove the algebraic identity </li></ul><ul><li>a 3 +b 3 =(a+b)(a 2 -ab+b 2 ) </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. Step2. To represent (b) 3 take a cube of dimension b x b x b i.e. 1x1x1 cubic units.
  6. 6. Step3. To represent a 3 +b 3 add a cube of dimension b x b x b i.e. 1x1x1 to the cube formed in the step 1 of dimension a x a x a i. e 3x3x3 cubic units. + =
  7. 7. Step4. To represent (a+b)a 2 make a cuboid of dimension (a +b) x a x a i.e. 4x3x3 cubic units.
  8. 8. Step5. To represent (a+b)a 2 +(a+b)b 2 add a cuboid of dimension (a +b) x b x b i. e 4 x1 x 1 to the cuboid formed in the previous step.
  9. 9. Step6. To represent (a+b)a 2 +(a+b)b 2 -(a+b)ab extract a cuboid of dimension (a+b) x a x b i.e. 4x3x1 cubic units from the shape formed in the previous step..
  10. 10. Step7. Rearrange the unit cubes left to form the shape formed in the Step 3.
  11. 11. Observe the following <ul><li>The number of unit cubes in a 3 = …27….. </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 +b 3 = …28….. </li></ul><ul><li>The number of unit cubes in (a+b)a 2 =…36…… </li></ul><ul><li>The number of unit cubes in (a+ b) a b=…12…… </li></ul><ul><li>The number of unit cubes in (a+b)b 2 =…4…… </li></ul><ul><li>The number of unit cubes in (a+b)a 2 _ (a+ b) a b + (a+b)b 2 </li></ul><ul><li>= …28…… </li></ul>
  12. 12. It is observed that the number of unit cubes in a 3 +b 3 is equal to the number of unit cubes in (a+b)a 2 -(a+b)ab+(a+b)b 2 i.e. (a+b)(a 2 -ab+b 2 ). Learning Outcome
  13. 13. Acknowledgement <ul><li>I would like to thank my sister who has helped me to click these picture from the mobile and then transferring to the computer. </li></ul>
  14. 14. Thank You
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