Write the following in the expanded form:$ (x+2 y+4 z)^{2} $

Given:

\( (x+2 y+4 z)^{2} \)

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,

$(x+2 y+4 z)^{2}=(x)^{2}+(2 y)^{2}+(4 z)^{2}+2 \times x \times 2 y+2 \times 2 y \times 4 z+2 \times 4 z \times x$

$=x^{2}+4 y^{2}+16 z^{2}+4 x y+16 y z+8 z x$

Hence, $(x+2 y+4 z)^{2}=x^{2}+4 y^{2}+16 z^{2}+4 x y+16 y z+8 z x$.

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Updated on: 10-Oct-2022

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