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Simplify. (7a − 6b + 5c)2 + (7a + 6b − 5c)2 - SSC (English Medium) Class 8 - Mathematics

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Question

Simplify.

(7a − 6b + 5c)+ (7a + 6b − 5c)2

Solution

It is known that,

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

\[\  \left( 7a - 6b + 5c \right)^2  +  \left( 7a + 6b - 5c \right)^2 \] 

\[ =  \left( 7a \right)^2  +  \left( - 6b \right)^2  +  \left( 5c \right)^2  + 2 \times 7a \times \left( - 6b \right) + 2 \times \left( - 6b \right) \times 5c + 2 \times 5c \times 7a +  \left( 7a \right)^2  +  \left( 6b \right)^2  +  \left( - 5c \right)^2  + 2 \times 7a \times 6b + 2 \times 6b \times \left( - 5c \right) + 2 \times \left( - 5c \right) \times 7a\] 

\[ = 49 a^2  + 36 b^2  + 25 c^2  - 84ab - 60bc + 70ca + 49 a^2  + 36 b^2  + 25 c^2  + 84ab - 60bc - 70ca\] 

\[ = 98 a^2  + 72 b^2  + 50 c^2  - 120bc\]

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APPEARS IN

 Balbharati Solution for Balbharati Class 8 Mathematics (2019 to Current)
Chapter 5: Expansion formulae
Practice Set 5.4 | Q: 2.3 | Page no. 28
Solution Simplify. (7a − 6b + 5c)2 + (7a + 6b − 5c)2 Concept: Expansion of (A + B + C)2.
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