Evaluate: $(4 a + b + 2 c)^{2}$

16 a^{2} + b^{2} + 4 c^{2} + 8 a b + 4 b c + 16 a c

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16 a^{2} + b^{2} + 4 c^{2} + 8 a b + 4 b c + 4 a c

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16 a^{2} + b^{2} + 4 c^{2} + 8 a b + 8 b c + 16 a c

No worries! We‘ve got your back. Try BYJU‘S free classes today!

16 a^{2} + b^{2} + c^{2} + 8 a b + 4 b c + 16 a c

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Solution

The correct option is A $16 a^{2} + b^{2} + 4 c^{2} + 8 a b + 4 b c + 16 a c$
$(4 a + b + 2 c)^{2}$
Using $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 a c$
$= (4 a)^{2} + b^{2} + (2 c)^{2} + 2 \times 4 a \times b + 2 \times b \times 2 c + 2 \times 4 a \times 2 c$
$= 16 a^{2} + b^{2} + 4 c^{2} + 8 a b + 4 b c + 16 a c$

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