Evaluate: $(3 a + 5 b + c)^{2}$

9 a^{2} + 25 b^{2} + c^{2} + 30 a b + 10 b c + 6 a c

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9 a^{2} + 25 b^{2} + c^{2} + 90 a b + 10 b c + 6 a c

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a^{2} + 25 b^{2} + c^{2} 30 a b + 10 b c + 6 a c

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a^{2} + 25 b^{2} + c^{2} 30 a b + 10 b c + a c

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Solution

The correct option is A $9 a^{2} + 25 b^{2} + c^{2} + 30 a b + 10 b c + 6 a c$
Given: $(3 a + 5 b + c)^{2}$
Using the identity: $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 a c$
$(3 a + 5 b + c)^{2} = (3 a)^{2} + (5 b)^{2} + c^{2} + 2 \times 3 a \times 5 b + 2 \times 5 b \times c + 2 \times 3 a \times c$
$(3 a + 5 b + c)^{2} = 9 a^{2} + 25 b^{2} + c^{2} + 30 a b + 10 b c + 6 a c$

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