Expand the following, using suitable identity.
$(2 a - 3 b - c)^{2}$

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Solution

We have, $(2 a - 3 b - c)^{2}$
Using identity
$(a + b + c)^{2}$ $= a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a,$
we get
$∴ (2 a - 3 b - c)^{2}$

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

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

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