Information about Unit-cubes Activity3 By Ms. Rashmi Kathuria

Published on November 1, 2007

Author: kulachihansraj

Source: slideshare.net

This is an activity to verify the cubic algebraic formula for

a^3-b^3.

a^3-b^3.

Activity 3 Aim : To prove the algebraic identity a 3 -b 3 =(a-b)(a 2 +ab+b 2 ) using unit cubes. Material required: Unit Cubes.

Aim : To prove the algebraic identity

a 3 -b 3 =(a-b)(a 2 +ab+b 2 )

using unit cubes.

Material required: Unit Cubes.

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 of dimension a x ax a i. e 3x3x3 cubic units. - =

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 3 ,4 and 5. + + =

Observe the following The number of unit cubes in a 3 = …27….. The number of unit cubes in b 3 = …1….. The number of unit cubes in a 3 –b 3 = …26….. The number of unit cubes in (a-b)a 2 =…18… The number of unit cubes in (a-b )a b=…6…… The number of unit cubes in (a-b)b 2 =…2…… The number of unit cubes in (a-b)a 2 + (a- b) a b + (a-b)b 2 = …26……

The number of unit cubes in a 3 = …27…..

The number of unit cubes in b 3 = …1…..

The number of unit cubes in a 3 –b 3 = …26…..

The number of unit cubes in (a-b)a 2 =…18…

The number of unit cubes in (a-b )a b=…6……

The number of unit cubes in (a-b)b 2 =…2……

The number of unit cubes in (a-b)a 2 + (a- b) a b + (a-b)b 2

= …26……

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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