Find the square root of:
$4 a^{2} + 9 b^{2} + c^{2} - 12 a b + 6 b c - 4 a c$

(2a + 3b - c)

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(2a - 3b + c)

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(-2a + 3b + c)

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(-2a + 3b + c)

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Solution

The correct option is C (-2a + 3b + c)
$4 a^{2} + 9 b^{2} + c^{2} - 12 a b + 6 b c - 4 a c$
$= (- 2 a)^{2} + (3 b)^{2} + c^{2} + 2 \times (- 2 a) \times 3 b + 2 \times 3 b \times c + 2 \times (- 2 a) \times c$
$= (- 2 a + 3 b + c)^{2}$
$[U s i n g (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 a c]$
$∴$ Required square root $= - 2 a + 3 b + c$

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Similar questions

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Factorise:
$4 a^{2} - 9 b^{2} - 2 a - 3 b$

4 a^{2} + 12 a b + 91 b^{2} - 25 c^{2}

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