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Simplify: (3a + 5b)3 − (3a − 5b)3 - SSC (English Medium) Class 8 - Mathematics

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Question

Simplify:

(3a + 5b)− (3a − 5b)3

Solution

It is known that,

\[a^3  -  b^3  = \left( a - b \right)\left( a^2 + b^2 + ab \right)\]\[\   \left( 3a + 5b \right)^3  -  \left( 3a - 5b \right)^3 \] \[ = \left\{ \left( 3a + 5b \right) - \left( 3a - 5b \right) \right\}\left\{ \left( 3a + 5b \right)^2 + \left( 3a - 5b \right)^2 + \left( 3a + 5b \right)\left( 3a - 5b \right) \right\}\] \[ = 10b\left( 9 a^2 + 25 b^2 + 30ab + 9 a^2 + 25 b^2 - 30ab + 9 a^2 - 25 b^2 \right)\] \[ = 10b\left( 27 a^2 + 25 b^2 \right)\]

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APPEARS IN

 Balbharati Solution for Balbharati Class 8 Mathematics (2019 to Current)
Chapter 6: Factorisation of Algebraic expressions
Practice Set 6.3 | Q: 2.2 | Page no. 32
Solution Simplify: (3a + 5b)3 − (3a − 5b)3 Concept: Factors of A3 - B3.
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