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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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