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Simplify: (3xy − 2ab)3 − (3xy + 2ab)3 - SSC (English Medium) Class 8 - Mathematics

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Question

Simplify:

(3xy − 2ab)3 − (3xy + 2ab)3

Solution

It is known that,

\[a^3  -  b^3  = \left( a - b \right)\left( a^2 + b^2 + ab \right)\]

\[\   \left( 3xy - 2ab \right)^3  -  \left( 3xy + 2ab \right)^3 \] 

\[ = \left\{ \left( 3xy - 2ab \right) - \left( 3xy + 2ab \right) \right\}\left\{ \left( 3xy - 2ab \right)^2 + \left( 3xy + 2ab \right)^2 + \left( 3xy - 2ab \right)\left( 3xy + 2ab \right) \right\}\] 

\[ = \left( - 4ab \right)\left( 9 x^2 y^2 + 4 a^2 b^2 - 12abxy + 9 x^2 y^2 + 4 a^2 b^2 + 12abxy + 9 x^2 y^2 - 4 a^2 b^2 \right)\] 

\[ = \left( - 4ab \right)\left( 27 x^2 y^2 + 4 a^2 b^2 \right)\] 

\[ =  - 108 x^2  y^2 ab - 16 a^3  b^3\]

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APPEARS IN

 Balbharati Solution for Balbharati Class 8 Mathematics (2019 to Current)
Chapter 6: Factorisation of Algebraic expressions
Practice Set 6.3 | Q: 2.5 | Page no. 32
Solution Simplify: (3xy − 2ab)3 − (3xy + 2ab)3 Concept: Factors of A3 - B3.
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