Your SlideShare is downloading. ×
0
Unit-cubes Activity3 By Ms. Rashmi Kathuria
Unit-cubes Activity3 By Ms. Rashmi Kathuria
Unit-cubes Activity3 By Ms. Rashmi Kathuria
Unit-cubes Activity3 By Ms. Rashmi Kathuria
Unit-cubes Activity3 By Ms. Rashmi Kathuria
Unit-cubes Activity3 By Ms. Rashmi Kathuria
Unit-cubes Activity3 By Ms. Rashmi Kathuria
Unit-cubes Activity3 By Ms. Rashmi Kathuria
Unit-cubes Activity3 By Ms. Rashmi Kathuria
Unit-cubes Activity3 By Ms. Rashmi Kathuria
Unit-cubes Activity3 By Ms. Rashmi Kathuria
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Text the download link to your phone
Standard text messaging rates apply

Unit-cubes Activity3 By Ms. Rashmi Kathuria

1,127

Published on

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

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

Published in: Education, Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
1,127
On Slideshare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
12
Comments
0
Likes
0
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide

Transcript

  • 1. Algebraic Identities.. By RASHMI KATHURIA
  • 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. 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. 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. Step3. To represent (a-b)a 2 make a cuboid of dimension (a-b) x a x a i.e. 2x3x3 cubic units.
  • 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. Step5. To represent (a-b)b 2 make a cuboid of dimension (a-b) x b x b i.e. 2x1x1 cubic units.
  • 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. 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. 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

×