Question

Please solve this problem by using x²-y² identity

(x+y+z)² -(x+y-z)²

Answer 1

$\large{\mathbf{HELLO \: \: DEAR,}} \\ \\ \\ \mathbf{(x^2 - y^2) = (x - y)(x + y)} \\ \\ \mathbf{[(x + y )+ z]^2 - [(x + y) - z]^2} \\ \\ \mathbf{[x^2 + y^2 + 2xy + z^2] - [x^2 + y^2 + 2xy - z^2]}\\ \\ \mathbf{[x^2 - x^2 + y^2 - y^2 + 2xy - 2xy + z^2 + z^2]} \\ \\ \mathbf{[ 2z^2]} \\ \\ \\ \large{\mathbf{\underline{I \: \: HOPE \: \: ITS \: \: HELP \: \: YOU \: \: DEAR, \: \: THANKS}}}$

Answer 2

$Heya$‼

$As\:we\:know:$
$x^2-y^2=(x+y)(x-y)$

$Given\:problem: (x+y+z)^2-(x+y-z)^2$

$SOLUTION:-$
$(x+y+z)^2-(x+y-z)^2$
$=[(x+y)+z]^2-[(x+y)-z]^2$
$=(x^2+2xy+y^2+z^2)-(x^2+2xy+y^2+z^2$
$=x^2+2xy+y^2+z^2-x^2-2xy-y^2-z^2$
$=x^2-x^2+2xy-2xy+y^2-y^2+z^2-z^2$
$=0$