Write the following in the expanded form:$ (2 a-3 b-c)^{2} $

Given:

\( (2 a-3 b-c)^{2} \)

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,

$(2 a-3 b-c)^{2}=(2 a)^{2}+(-3 b)^{2}+(-c)^{2}+2 \times 2 a \times-3 b+2 \times-3 b \times-c+2 \times-c \times 2 a$

$=4 a^{2}+9 b^{2}+c^{2}-12 a b+6 b c-4 c a$

Hence, $(2 a-3 b-c)^{2}=4 a^{2}+9 b^{2}+c^{2}-12 a b+6 b c-4 c a$.

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Updated on: 10-Oct-2022

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