Factorise: $144 b^{2} - 72 b c + {9 c}^{2}$

3 (4 b - c) (4 b + c)

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9 (4 b - c) (4 b + c)

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9 (4 b - c) (4 b - c)

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3 (4 b - c) (4 b - c)

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Solution

The correct option is C $9 (4 b - c) (4 b - c)$
$144 b^{2} - 72 b c + {9 c}^{2}$

$= {(12 b)}^{2} - 2 (12 b) (3 c) + {(3 c)}^{2}$

$= {(12 b - 3 c)}^{2}$ ... $[∵ {(a - b)}^{2} = a^{2} - 2 a b + b^{2}]$

$= {[3 (4 b - c)]}^{2}$

$= {9 (4 b - c)}^{2}$

$= 9 (4 b - c) (4 b - c)$

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Factorise: 144b2−72bc+9c2

The correct option is C 9(4b−c)(4b−c)144b2−72bc+9c2=(12b)2−2(12b)(3c)+(3c)2=(12b−3c)2 ...[∵(a−b)2=a2−2ab+b2]=[3(4b−c)]2=9(4b−c)2=9(4b−c)(4b−c)

Factorise: $144 b^{2} - 72 b c + {9 c}^{2}$

The correct option is C $9 (4 b - c) (4 b - c)$
$144 b^{2} - 72 b c + {9 c}^{2}$

$= {(12 b)}^{2} - 2 (12 b) (3 c) + {(3 c)}^{2}$

$= {(12 b - 3 c)}^{2}$ ... $[∵ {(a - b)}^{2} = a^{2} - 2 a b + b^{2}]$

$= {[3 (4 b - c)]}^{2}$

$= {9 (4 b - c)}^{2}$

$= 9 (4 b - c) (4 b - c)$