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Simplify (3r − 2k)3 + (3r + 2k)3 - SSC (English Medium) Class 8 - Mathematics

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Question

Simplify

(3r − 2k)3 + (3r + 2k)3

Solution

It is known that,

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

\[\left( 3r - 2k \right)^3 + \left( 3r + 2k \right)^3 \]
\[ = \left( 3r \right)^3 - \left( 2k \right)^3 - 3 \times \left( 3r \right)^2 \times 2k + 3 \times 3r \times \left( 2k \right)^2 + \left( 3r \right)^3 + \left( 2k \right)^3 + 3 \times \left( 3r \right)^2 \times 2k + 3 \times 3r \times \left( 2k \right)^2 \]
\[ = 27 r^3 - 8 k^3 - 54 r^2 k + 36r k^2 + 27 r^3 + 8 k^3 + 54 r^2 k + 36r k^2 \]
\[ = 54 r^3 + 72r k^2\]

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APPEARS IN

 Balbharati Solution for Balbharati Class 8 Mathematics (2019 to Current)
Chapter 5: Expansion formulae
Practice Set 5.3 | Q: 2.2 | Page no. 27
Solution Simplify (3r − 2k)3 + (3r + 2k)3 Concept: Expansion of (A + B + C)2.
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