Question

Fasssssssssssssssssst!
What is a-b-c whole square?

Answer 1

we know that (a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca                                                              (a-b-c)^2=a^2+(-b)^2+(-c)^2+2(a)(-b)+2(-b)(-c)+2(-c)(a)
=a^2+b^2+c^2-2ab+2bc-2ca

Answer 2

Answer:

The formula for $( a - b - c ) ^ { 2 } = a ^ { 2 } + b ^ { 2 } + c ^ { 2 } - 2 a b + 2 b c - 2 c a$

Solution:

Given that

$(a-b-c)^2$

We know the algebraic identity,

$( x + y + z ) ^ { 2 }$

$= x ^ { 2 } + y ^ { 2 } + z ^ { 2 } + 2 x y + 2 y z + 2 z x$

Now,

$\begin{array} { l } { ( a - b - c ) ^ { 2 } } \\\\ { = \left[ a ^ { 2 } + ( - b ) ^ { 2 } + ( - c ) ^ { 2 } \right] ^ { 2 } } \\\\ { = a ^ { 2 } + ( - b ) ^ { 2 } + ( - c ) ^ { 2 } + 2 a ( - b ) + 2 ( - b ) ( - c ) + 2 ( - c ) a } \\\\ { = a ^ { 2 } + b ^ { 2 } + c ^ { 2 } - 2 a b + 2 b c - 2 c a } \end{array}$

The formula for $( a - b - c ) ^ { 2 } = a ^ { 2 } + b ^ { 2 } + c ^ { 2 } - 2 a b + 2 b c - 2 c a$