Factorise:
$a^{2} b^{2} - 6 a b c + 9 c^{2}$

(a b - 3 a b c)^{2}

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(b - 3 c)^{2}

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(a - 3 c)^{2}

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(a b - 3 c)^{2}

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Solution

The correct option is D $(a b - 3 c)^{2}$
$a^{2} b^{2} - 6 a b c + 9 c^{2}$
$= (a b)^{2} + 2 \times a b \times (- 3 c) + (- 3 c)^{2}$
Using $a^{2} + b^{2} - 2 a b = (a - b)^{2}$
$= (a b - 3 c)^{2}$

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