Simplify: $(5 a - 5 b - 5 c)^{2}$

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Solution

We know that $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$
Here, $a = 5 a, b = - 5 b, c = - 5 c$
$(5 a - 5 b - 5 c)^{2} = (5 a)^{2} + (- 5 b)^{2} + (- 5 c)^{2} + 2.5 a . (- 5 b) + 2. (- 5 b) . (- 5 c) + 2. (- 5 c) .5 a$
$=$ $25 a^{2} + 25 b^{2} + 25 c^{2} - 50 a b + 50 b c - 50 a c$
Therefore, $(5 a - 5 b - 5 c)^{2} = 25 a^{2} + 25 b^{2} + 25 c^{2} - 50 a b + 50 b c - 50 a c$

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