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Simplify the Following Expressions: (X + Y - 2z)^2 - X^2 - Y^2 - 3z^2 +4xy - Mathematics

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Question

Simplify the following expressions:

`(x + y - 2z)^2 - x^2 - y^2 - 3z^2 +4xy`

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Solution

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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Chapter 4: Algebraic Identities - Exercise 4.2 [Page 12]

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RD Sharma Mathematics [English] Class 9
Chapter 4 Algebraic Identities
Exercise 4.2 | Q 7.2 | Page 12

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