Factorize the Following Expressions: A3 + 3a2b + 3ab2 + B3 - 8 - Mathematics

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Factorize the following expressions:

a3 + 3a2b + 3ab2 + b3 - 8

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Solution

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

= (a + b)3 - 23

= (a + b - 2)((a + b)2 + (a + b)2 + 22)

= (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 5.2 [Page 14]

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RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Exercise 5.2 | Q 23 | Page 14

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