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Simplify : M 2 − N 2 ( M + N ) 2 × M 2 + M N + N 2 M 3 − N 3 - SSC (English Medium) Class 8 - Mathematics

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Question

Simplify :

\[\frac{m^2 - n^2}{\left( m + n \right)^2} \times \frac{m^2 + mn + n^2}{m^3 - n^3}\]

Solution

It is known that,

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

\[\left( 1 \right)  \frac{m^2 - n^2}{\left( m + n \right)^2} \times \frac{m^2 + mn + n^2}{m^3 - n^3}\] 

\[ =   \frac{\left( m + n \right)\left( m - n \right)}{\left( m + n \right)\left( m + n \right)} \times \frac{\left( m^2 + mn + n^2 \right)}{\left( m - n \right)\left( m^2 + mn + n^2 \right)}\] 

\[ =   \frac{1}{m + n}\]

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APPEARS IN

 Balbharati Solution for Balbharati Class 8 Mathematics (2019 to Current)
Chapter 6: Factorisation of Algebraic expressions
Practice Set 6.4 | Q: 1 | Page no. 33
Solution Simplify : M 2 − N 2 ( M + N ) 2 × M 2 + M N + N 2 M 3 − N 3 Concept: Factors of A3 - B3.
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