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Simplify: (A + B)3 − A3 − B3 - SSC (English Medium) Class 8 - Mathematics

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Question

Simplify:

(a + b)− a− b3

Solution

It is known that,

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

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

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

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

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

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

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

\[ = 3 a^2 b + 3a b^2 \]

  Is there an error in this question or solution?

APPEARS IN

 Balbharati Solution for Balbharati Class 8 Mathematics (2019 to Current)
Chapter 6: Factorisation of Algebraic expressions
Practice Set 6.3 | Q: 2.3 | Page no. 32
Solution Simplify: (A + B)3 − A3 − B3 Concept: Factors of A3 - B3.
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