Question

simplify the following expression (x+y+z)(x+y-z)​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given data: $(x+y+z)(x+y-z)$

To Find: The simplified expression for the given expression $(x+y+z)(x+y-z)$.

Solution:

Consider the expression $(x+y+z)(x+y-z)$,

Multiply $x$ with $(x+y-z)$, $y$ with $(x+y-z)$ and $z$ with $(x+y-z)$,

$=(x^{2} +xy-xz)+(yx+y^{2}-yz)+(zx+zy-z^{2} )$

By removing the brackets, the expression can be written as,

$=x^{2} +xy-xz+yx+y^{2}-yz+zx+zy-z^{2}$

Arrange the terms in alphabetical order,

$=x^{2} +y^{2}-z^{2}+xy+xy-xz+xz-yz+yz$

Evaluate,

$=x^{2} +y^{2}-z^{2}+2xy+0+0$

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

Therefore, the simplified expression for the given expression$(x+y+z)(x+y-z)$ is $x^{2} +y^{2}-z^{2}+2xy$.