Page 25 - Mathematics Class - IX

3. Now, arrange the cubes and cuboids as shown in Fig. (c).

b b a – b b
a – b b

a

a

a – b b
Fig. (c)

OBSERVATIONS
Sum of volumes of cubes and cuboids in Figs. (a) and (b).

= (a – b) + 3(a – b) (ab) + b 3 ...(i)
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In Fig. (c), we observe that it is cube of side a
\ Volume of cube = a cubic units ...(ii)
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From (i) and (ii), we get
(a – b) + 3ab (a – b) + b = a 3
3
3
or (a – b) = a – 3ab(a – b) – b 3
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3
INFERENCE

This verify the identity: (a – b) = a – 3ab(a – b) – b 3
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EXTENDED TASK
1. Verify the identity (x – y) = x – 3x y + 3xy – y by taking x = 7 and y = 3.
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2. Using the identity (a – b) = a – 3ab(a – b) – b , make 5 multiple-choice questions.
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APPLICATION
The result can be used in
1. Calculating cube of a number expressed as a difference of two numbers.

2. Simplification and factorisation of algebraic expressions.

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