Question
Simplify:$(x + y - z)^2 + (x - y + z)^2$
✓
Answer
$(x + y - z)^2 + (x - y + z)^2$
$= x^2 + y^2 + z^2 + 2(x)(y) + 2(y)(-z) + 2(x)(-z) + x^2 + y^2 + z^2 + 2(x)(-y) + 2(-y) + 2(x)(z)$
$= x^2+ y^2 + z^2 + 2xy - 2yz - 2xz + x^2 + y^2 + z^2 - 2xy - 2yz + 2xz$
$= 2x^2 + 2y^2 + 2z^2- 4yz.$
$= x^2 + y^2 + z^2 + 2(x)(y) + 2(y)(-z) + 2(x)(-z) + x^2 + y^2 + z^2 + 2(x)(-y) + 2(-y) + 2(x)(z)$
$= x^2+ y^2 + z^2 + 2xy - 2yz - 2xz + x^2 + y^2 + z^2 - 2xy - 2yz + 2xz$
$= 2x^2 + 2y^2 + 2z^2- 4yz.$
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