Find the value of $‘ M^{'}$ if $(11 p q + 4 q)^{2} - (11 p q - 4 q)^{2} = M p q^{2}$ .

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132

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176

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Solution

The correct option is D 176
$(11 p q + 4 q)^{2} - (11 p q - 4 q)^{2}$
$= (11 p q + 4 q + 11 p q - 4 q) \times (11 p q + 4 q - 11 p q + 4 q$

[Using $a^{2} - b^{2} = (a - b) (a + b)$ , here $a = 11 p q + 4 q$ and $b = 11 p q - 4 q$ ]

$= (22 p q) (8 q) = 176 p q^{2}$

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