Write the following in the expanded form:$ (-2 x+3 y+2 z)^{2} $

Given:

\( (-2 x+3 y+2 z)^{2} \)

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,

$(-2 x+3 y+2 z)^{2}=(-2 x)^{2}+(3 y)^{2}+(2 z)^{2}+2 \times(-2 x) \times 3 y+2 \times 3 y \times 2 z+2 \times 2 z \times(-2 x)$

$=4 x^{2}+9 y^{2}+4 z^{2}-12 x y+12 y z-8 z x$

Hence, $(-2 x+3 y+2 z)^{2}=4 x^{2}+9 y^{2}+4 z^{2}-12 x y+12 y z-8 z x$.

Tutorialspoint

Updated on: 10-Oct-2022

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