simplify the expression
$$ (x+y-z) (x-y+z) -(x+y+z)(x-y-z) $$

Question

simplify the expression 
$$ (x+y-z) (x-y+z) -(x+y+z)(x-y-z) $$

Uniteasy Admin · Accepted Answer

Group terms to apply the formula for the difference of squares 
$$ (x+y-z) (x-y+z) -(x+y+z)(x-y-z) $$
$$=[x+(y-z)] [x-(y-z)] -[x+(y+z)][x-(y+z) ]$$
$$=x^2-(y-z)^2-x^2+(y+z)^2$$
$$=(y+z)^2-(y-z)^2$$
$$=(y+z+y-z)(y+z-y+z)$$
$$=4yz$$

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