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Simplify (4a − 3)3 − (4a +3)3 - SSC (English Medium) Class 8 - Mathematics

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Question

Simplify

(4a − 3)− (4a +3)3

Solution

It is known that,

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

\[\ \left( 4a - 3 \right)^3  -  \left( 4a + 3 \right)^3 \] 

\[ =  \left( 4a \right)^3  -  \left( 3 \right)^3  - 3 \times  \left( 49 \right)^2  \times 3 + 3 \times 49 \times  \left( 3 \right)^2  - \left\{ \left( 49 \right)^3 + \left( 3 \right)^3 + 3 \times \left( 49 \right)^2 \times 3 + 3 \times 49 \times \left( 3 \right)^2 \right\}\] 

\[ = 64 a^3  - 27 - 144 a^2  + 108 - 64 a^3  - 27 - 144 a^2  - 108\] 

\[ =  - 54 - 288 a^2\]

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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: 2.3 | Page no. 27
Solution Simplify (4a − 3)3 − (4a +3)3 Concept: Expansion of (A + B + C)2.
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