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

Given:

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

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,

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

$=4+x^{2}+4 y^{2}+4 x-4 x y-8 y$

Hence, $(2+x-2 y)^{2}=4+x^{2}+4 y^{2}+4 x-4 x y-8 y$.