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प्रश्न
Simplify the following expressions:
`(x + y - 2z)^2 - x^2 - y^2 - 3z^2 +4xy`
उत्तर
We have,
`(x + y - 2z)^2 - x^2 - y^2 - 3z^2 +4xy`
`=[x^2 + y^2 + (-2z)^2 + 2xy + 2(y)(-2z)] - x^2 - y^2 - 3z^2 + 4xy`
`= x^2 + y^2 + 4z^2 + 2xy - 4yz - x^2 - y^2 - 3z^2 = 4xy`
`= z^2 + 6xy - 4yz - 4zx`
`∴ (x + y - 2z)^2 - x^2 - y^2 - 3z^2 + 4xy = z^2 + 6xy - 4yz - 4zx`
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