Maharashtra State BoardSSC (English Medium) 8th Standard
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Factorise: 27m3 − 216n3 - Mathematics

Sum

Factorise:

27m− 216n3

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Solution

It is known that,

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

\[\ 27 m^3  - 216 n^3 \] 

\[ = 27\left[ m^3 - 8 n^3 \right]\] 

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

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

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

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APPEARS IN

Balbharati Mathematics 8th Standard Maharashtra State Board
Chapter 6 Factorisation of Algebraic expressions
Practice Set 6.3 | Q 1.3 | Page 32
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