Question

(x-2y-z)² Expansion​

Answer 1

x^2+4y^2+z^2-4xy+4yz++2xz

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Answer 2

Question :

Expand (x-2y-z)² .

Answer :

x^2 + 4y^2 + z^2 - 4xy + 4yz - 2xz is the answer.

Given :

The expression (x-2y-z)²

To find :

The expansion of the given expression

Solution :

The expression is (x-2y-z)²

We know that ,

(a+b+c)^2 = a^2 + b^2 + c^2 + 2 ( ab + bc + ca )

Here, a = x

b = -2y

c = -z

Hence, (x-2y-z)² will be ,

= x^2 + (-2y)^2 + (-z)^2 + 2 ( x × (-2y) + (-2y × -z) + (-z × x))

= x^2 + 4y^2 + z^2 + 2( -2xy + 2yz - xz)

= x^2 + 4y^2 + z^2 - 4xy + 4yz - 2xz

Hence, the expansion of the given expression (x-2y-z)² is x^2 + 4y^2 + z^2 - 4xy + 4yz - 2xz.

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