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# Simplify : (X + Y)3 − (X − Y)3 - Mathematics

Sum

Simplify :

(x + y)− (x − y)3

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#### 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 Mathematics 8th Standard Maharashtra State Board
Chapter 6 Factorisation of Algebraic expressions
Practice Set 6.3 | Q 2.1 | Page 32
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