Question
Simplify the following expressions:
$(x+y-2 z)^2-x^2-y^2-3 z^2+4 x y$
$(x+y-2 z)^2-x^2-y^2-3 z^2+4 x y$
✓
Answer
Expanding, we get
$(x+y-2 z)^2-x^2-y^2-3 z^2+4 x y$
$=\left[x^2+y^2+4 z^2+2 x y+2 y(-2 z)+2 a(-2 c)\right]-x^2-y^2-3 z^2+4 x y$
$=z^2+6 x y-4 y z-4 z x$
$(x+y-2 z)^2-x^2-y^2-3 z^2+4 x y=z^2+6 x y-4 y z-4 z x$
$(x+y-2 z)^2-x^2-y^2-3 z^2+4 x y$
$=\left[x^2+y^2+4 z^2+2 x y+2 y(-2 z)+2 a(-2 c)\right]-x^2-y^2-3 z^2+4 x y$
$=z^2+6 x y-4 y z-4 z x$
$(x+y-2 z)^2-x^2-y^2-3 z^2+4 x y=z^2+6 x y-4 y z-4 z x$
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