Page 31 - Mathematics Class - IX

4. Take the shape obtained by removing b from a and show that it splits into three cuboids of dimensions
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obtained in the above step (Fig. (d)).

Fig. (d)
OBSERVATIONS

1. No. of unit cubes in a = 27 4. No. of unit cubes in (a – b) a = 18
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2. No. of unit cubes in b = 1 5. No. of unit cubes in (a – b) (ab) = 6
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3. No. of unit cubes in a – b = 26 6. No. of unit cubes in (a – b) b = 2
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7. No. of unit cubes in (a – b) a + (a – b) (ab) + (a – b) b = 18 + 6 + 2 = 26
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INFERENCE
It is verified that, a – b = (a – b) a + (a – b)ab + (a – b) b = (a – b) (a + ab + b )
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EXTENDED TASK
1. Verify the identify a – b = (a – b) (a + ab + b ) for a = 7, b = 3 units.
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2. Prepare a chart to bring out the significant features of 2D shapes and 3D solids.
APPLICATION
The identity can be used in simplification/factorisation of algebraic expressions.
Viva-Voce

1. x – y ?
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Ans. x – y = (x – y) (x + xy + y )
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2. What is the volume of a cube of side 1 cm?
Ans. 1 cm 3
3. Find the value of 6 – 1 using identity a – b = (a – b) (a + ab + b ).
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Ans. (6 – 1) (36 + 6 + 1) = 5 × 43 = 215
4. How many dimensions does a cube or a cuboid have?
Ans. Three dimensions namely length, breadth and height.
5. What will be the volume of a cube of 27 cubic units if a cube of 2 units is cut off from it?
Ans. 27 – 8 = 19 cubic units.
6. Is a – 4 a factor of a + 64?
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Ans.  a + 64 = 0
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a = –64
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a = (–4) ⇒ a = –4 or a + 4 is the factor of a + 64.
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So, we can say that a – 4 is not that factor of a + 64.
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