Question

simplify (x+y+z)^2+(x+y-z)^2​

Answer 1

Answer:

(x+y+z)^2 +( x+ y-z)^2

= x^2 + y^2 + z^2 + 2xy + 2yz + 2zx

+ x^2 + y^2 + z^2 + 2xy - 2yz - 2zx

= 2x^2 + 2y^2 + 2z^2 + 4xy

= 2( x^2 + y^2 + z^2 + 2xy)

Answer 2

Answer:

Given Question.....

( x + y + z ) ^2 + ( x+ y - z )^2

By using the formula of ........

( a + b + c )^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca

Let....

x = a

y = b

z = c

( x + y + z ) ^2 + ( x + y - z ) ^2

= [ x + y + z ]^2 + [ x + y + ( - z ) ]^2

= x^2 + y^2 + z^2 + 2xy + 2yz + 2zx +

x^2 + y^2 + z^2 + 2xy - 2yz - 2zx

= 2x^2 + 2y^2 + 2z^2 + 4xy

( By taking 2 as common.... )

= 2( x^2 + y^2 + z^2 + 2xy )