Factorise: $4 a^{2} + b^{2} + 25 c^{2} - 4 a b - 10 b c + 20 c a$

(2 a - b + 5 c) (2 a + b - 5 c)

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(2 a + b + 5 c) (2 a - b + 5 c)

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(2 a - b + 5 c) (2 a - b + 5 c)

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(2 a - b - 5 c) (2 a - b + 5 c)

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Solution

The correct option is C $(2 a - b + 5 c) (2 a - b + 5 c)$
$4 a^{2} + b^{2} + 25 c^{2} - 4 a b - 10 b c + 20 c a$
$= (2 a)^{2} + (- b)^{2} + (5 c)^{2} + 2 \times 2 a \times (- b) + 2 \times (- b) \times 5 c + 2 \times 5 c \times 2 a$
Using, $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$
$= (2 a - b + 5 c)^{2}$
$= (2 a - b + 5 c) (2 a - b + 5 c)$

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