Question

Simplify.

(7a − 6b + 5c)² + (7a + 6b − 5c)²

Answer 1

It is known that,

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

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

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

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

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