Expand the following, using suitable identities: ${(3 a - 7 b - c)}^{2}$

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Solution

Given ${(3 a - 7 b - c)}^{2}$
Using identity
${(x + y + z)}^{2} = x^{2} + y^{2} + z^{2} + 2 x y + 2 y z + 2 z$
Here, $x = 3 a, y = - 7 b, z = - c$
Therefore, ${(3 a - 7 b - c)}^{2} = (3 a)^{2} + {(- 7 b)}^{2} + {(- c)}^{2} + (2 \times 3 a \times - 7 b) + (2 \times - 7 b \times - c) + (2 \times - c \times 3 a)$
Hence, ${(3 a - 7 b - c)}^{2} = 9 a^{2} + 49 b^{2} + c^{2} - 42 a b + 14 b c - 6 c a$

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