Maharashtra State BoardSSC (English Medium) 8th Standard
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Simplify. (3k − 4r − 2m)2 − (3k + 4r − 2m)2 - Mathematics

Sum

Simplify.

(3k − 4r − 2m)− (3k + 4r − 2m)2

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Solution

It is known that,

\[\left( a + b + c \right)^2  =  a^2  +  b^2  +  c^2  + 2ab + 2bc + 2ca\]

\[\   \left( 3k - 4r - 2m \right)^2  -  \left( 3k + 4r - 2m \right)^2 \] 

\[ =  \left( 3k \right)^2  +  \left( - 4r \right)^2  +  \left( - 2m \right)^2  + 2 \times 3k \times \left( - 4r \right) + 2 \times \left( - 4r \right) \times \left( - 2m \right) + 2 \times \left( - 2m \right) \times 3k - \left\{ \left( 3k \right)^2 + \left( 4r \right)^2 + \left( - 2m \right)^2 + 2 \times 3k \times 4r + 2 \times 4r \times \left( - 2m \right) + 2 \times \left( - 2m \right) \times 3k \right\}\] \[ = 9 k^2  + 16 r^2  + 4 m^2  - 24kr + 16rm - 12mk - 9 k^2  - 16 r^2  - 4 m^2  - 24kr + 16rm + 12mk\] \[ = 32rm - 48kr\]

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APPEARS IN

Balbharati Mathematics 8th Standard Maharashtra State Board
Chapter 5 Expansion formulae
Practice Set 5.4 | Q 2.3 | Page 28
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