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Factorise: 27m3 − 216n3 - SSC (English Medium) Class 8 - Mathematics

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Question

Factorise:

27m− 216n3

Solution

It is known that,

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

\[\ 27 m^3  - 216 n^3 \] 

\[ = 27\left[ m^3 - 8 n^3 \right]\] 

\[ = 27\left[ \left( m \right)^3 - \left( 2n \right)^3 \right]\] 

\[ = 27\left[ \left( m - 2n \right)\left\{ \left( m \right)^2 + \left( 2n \right)^2 + \left( m \right) \times \left( 2n \right) \right\} \right]\] 

\[ = 27\left( m - 2n \right)\left( m^2 + 4 n^2 + 2mn \right)\]

  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: 1.3 | Page no. 32
Solution Factorise: 27m3 − 216n3 Concept: Factors of A3 - B3.
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