Algebraic Identities.. By  RASHMI KATHURIA
Activity 3 <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  a 3  - b 3   extract a cube of dimension b x b x b i.e. 1x1x1 from  the cube formed in the step 1 o...
Step3.   To represent  (a-b)a 2   make a cuboid of dimension (a-b) x a x a i.e. 2x3x3  cubic units.
Step4 .  To represent  (a-b) a b  make a cuboid of dimension (a-b) x a x b i.e. 2x3x1  cubic units.
Step5.   To represent  (a-b)b 2   make a cuboid of dimension (a-b) x b x b i.e. 2x1x1  cubic units.
Step6.   To represent  (a-b)a 2  +(a-b)ab+(a-b)b 2   I .e (a-b)(a 2 +ab+b 2 ) ,  join all the  cuboids formed in the Steps...
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...
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Usings unit cubes1

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

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Usings unit cubes1

  1. 1. Algebraic Identities.. By RASHMI KATHURIA
  2. 2. Activity 3 <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 a 3 - b 3 extract a cube of dimension b x b x b i.e. 1x1x1 from the cube formed in the step 1 of dimension a x ax a i. e 3x3x3 cubic units. - =
  6. 6. Step3. To represent (a-b)a 2 make a cuboid of dimension (a-b) x a x a i.e. 2x3x3 cubic units.
  7. 7. Step4 . To represent (a-b) a b make a cuboid of dimension (a-b) x a x b i.e. 2x3x1 cubic units.
  8. 8. Step5. To represent (a-b)b 2 make a cuboid of dimension (a-b) x b x b i.e. 2x1x1 cubic units.
  9. 9. Step6. To represent (a-b)a 2 +(a-b)ab+(a-b)b 2 I .e (a-b)(a 2 +ab+b 2 ) , join all the cuboids formed in the Steps 3 ,4 and 5. + + =
  10. 10. 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 = …26….. </li></ul><ul><li>The number of unit cubes in (a-b)a 2 =…18… </li></ul><ul><li>The number of unit cubes in (a-b )a b=…6…… </li></ul><ul><li>The number of unit cubes in (a-b)b 2 =…2…… </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>= …26…… </li></ul>
  11. 11. 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

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