uising unit cubes 2
DESCRIPTION
This is an activity to verify the formula a^3-b^3.TRANSCRIPT
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Algebraic Identities…
By RASHMI KATHURIA
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Activity 4
Aim : To prove the algebraic identity a3+b3 =(a+b)(a2 -ab+b2)
using unit cubes.
Material required: Unit Cubes.
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Start Working..
Take any suitable value for a and b. Let a=3 and b=1
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Step 1. To represent (a)3 make a cube of dimension a x a x a i.e. 3x3x3 cubic units.
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Step2. To represent (b)3 take a cube of dimension b x b x b i.e. 1x1x1 cubic units.
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Step3. To represent a3+b3 add a cube of dimension b x b x b i.e. 1x1x1to the cube formed in the step 1 of dimension a x a x a
i. e 3x3x3 cubic units.
+ =
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Step4. To represent (a+b)a2 make a cuboid of dimension (a +b) x a x a i.e. 4x3x3 cubic units.
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Step5. To represent (a+b)a2+(a+b)b2 add a cuboid ofdimension (a +b) x b x b i. e 4 x1 x 1 to the cuboid
formed in the previous step.
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Step6. To represent (a+b)a2+(a+b)b2-(a+b)ab extract a cuboid of dimension (a+b) x a x b
i.e. 4x3x1 cubic units from the shape formedin the previous step..
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Step7. Rearrange the unit cubes left to form the shape formed in the Step 3.
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Observe the following
The number of unit cubes in a3 = …27….. The number of unit cubes in b3 = …1….. The number of unit cubes in a3+b3 = …28….. The number of unit cubes in (a+b)a2=…36…… The number of unit cubes in (a+ b) a b=…12…… The number of unit cubes in (a+b)b2=…4…… The number of unit cubes in (a+b)a2_ (a+ b) a b +
(a+b)b2 = …28……
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It is observed that the number of unit cubes in a3+b3 is equal to the number of unit cubesin (a+b)a2 -(a+b)ab+(a+b)b2 i.e. (a+b)(a2-ab+b2).
Learning Outcome
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Acknowledgement
I would like to thank my sister who has helped me to click these picture from the mobile and then transferring to the computer.
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Thank You