Factorize A3 – 3a2b + 3ab2 – B3 + 8 - Mathematics

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Factorize  a3 – 3a2b + 3ab2 – b3 + 8

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Solution

a3 - 3a2b + 3ab2 - b3 + 8

= (a - b)3 + 8                          [∵ a3 - b3 - 3a2b + 3ab2 = (a - b)3 

= (a - b)3 + 23

= (a - b + 2)((a - b)2 - (a - b)2 + 22 )              [∵ a3 + b3  = (a + b)(a2 - ab + b2)]

= (a - b + 2)(a2 + b2 - 2ab - 2(a - b) + 4)

= (a - b + 2)(a2 + b2 - 2ab - 2a + 2b + 4)

∴ a3 - 3a2b + 3ab2  - b3 + 8 = (a - b + 2)(a2  + b2  - 2ab - 2a + 2b + 4)

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Chapter 5: Factorisation of Algebraic Expressions - Exercise 5.3 [Page 17]

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RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Exercise 5.3 | Q 5 | Page 17

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