Write the following in the expanded form:$ (2 x-y+z)^{2} $

Given:

\( (2 x-y+z)^{2} \)

To do:

We have to write the given expression in expanded form.

Solution:

We know that,

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

Therefore,

$(2 x-y+z)^{2}=(2 x)^{2}+(-y)^{2}+(z)^{2}+2 \times (2 x) \times(-y)+2 \times(-y) \times z+2 \times z \times 2 x$

$=4 x^{2}+y^{2}+z^{2}-4 x y-2 y z+4 z x$

Hence, $(2 x-y+z)^{2}=4 x^{2}+y^{2}+z^{2}-4 x y-2 y z+4 z x$.

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Updated on: 10-Oct-2022

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