SSC (English Medium) Class 8Maharashtra State Board
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Simplify : (X + Y)3 − (X − Y)3 - SSC (English Medium) Class 8 - Mathematics

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Question

Simplify :

(x + y)− (x − y)3

Solution

It is known that,

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

\[ = 2y\left( 3 x^2 + y^2 \right)\]

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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: 2.1 | Page no. 32
Solution Simplify : (X + Y)3 − (X − Y)3 Concept: Factors of A3 - B3.
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