$Factorise: 9 x^{2} - 24 x + 16$

(6 x - 4)^{2}

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(6 x + 4)^{2}

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(3 x + 4)^{2}

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(3 x - 4)^{2}

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Solution

The correct option is D $(3 x - 4)^{2}$
The given expression can be written as,
$9 x^{2} - 24 x + 16$
$= (3 x)^{2} - 2 (3 x) (4) + 4^{2}$
Comparing the above equation with the identity
$(a - b)^{2} = a^{2} - 2 a b + b^{2},$ we get
$9 x^{2} - 24 x + 16 = (3 x - 4)^{2}$

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