Write the following in the expanded form:$ (m+2 n-5 p)^{2} $

Given:

\( (m+2 n-5 p)^{2} \)

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,

$(m+2 n-5 p)^{2}=(m)^{2}+(2 n)^{2}+(-5 p)^{2}+2 \times m \times 2 n+2 \times(2 n) \times(-5 p)+2 \times(-5 p) \times m$

$=m^{2}+4 n^{2}+25 p^{2}+4 m n-20 n p-10 p m$

Hence,$(m+2 n-5 p)^{2}=m^{2}+4 n^{2}+25 p^{2}+4 m n-20 n p-10 p m$.