Factorize the Following Expressions: (A - 2b)3 - 512b3 - Mathematics

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Factorize the following expressions:

(a - 2b)3 - 512b3

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Solution

(a - 2b)3 - 512b3

= (a - 2b)3 - (8b)3

= (a - 2b - 8b)((a - 2b)2  + (a - 2b)8b + (8b)2)            [ ∵ a3 - b3 = (a - b)(a2 + ab + b2)]

= (a -10b)(a2  + 4b2  - 4ab + 8b (a - 2b) + (8b)2 )      [ ∵ (a - b)2 = a2 + b2 - 2ab]

= (a -10b)(a2   + 4b2   - 4ab + 8ab -16b2  + 64b2)

= (a = 10b)(a2 + 68b2 -16b2 - 4ab + 8ab)

= (a -10b)(a2 + 52b2 + 4ab)

∴ (a - 2b)3  - 512b3   = (a -10b)(a2  + 4ab + 52b2)

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Chapter 5: Factorisation of Algebraic Expressions - Exercise 5.2 [Page 14]

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RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Exercise 5.2 | Q 10 | Page 14

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