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Factorise. 24a3 + 81b3 - SSC (English Medium) Class 8 - Mathematics

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Question

Factorise.

24a+ 81b3

Solution

It is known that,

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

\[\  24 a^3  + 81 b^3 \] 

\[ = 3\left[ 8 a^3 + 27 b^3 \right]\] 

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

\[ = 3\left[ \left( 2a + 3b \right)\left\{ \left( 2a \right)^2 + \left( 3b \right)^2 - \left( 2a \right) \times \left( 3b \right) \right\} \right]\] 

\[ = 3\left( 2a + 3b \right)\left( 4 a^2 + 9 b^2 - 6ab \right)\]

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APPEARS IN

 Balbharati Solution for Balbharati Class 8 Mathematics (2019 to Current)
Chapter 6: Factorisation of Algebraic expressions
Practice Set 6.2 | Q: 5 | Page no. 31
Solution Factorise. 24a3 + 81b3 Concept: Factors of A3 + B3.
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