The value of $(7 x y + 3 x)^{2} - (7 x y - 3 x)^{2}$ is ____________.

84 x^{2} y

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98 x^{2} y^{2} + 18 x^{2} + 76 x^{2} y

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49 x^{2} y^{2} + 18 x^{2} + 84 x^{2} y

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42 x^{2} y

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Solution

The correct option is A $84 x^{2} y$
Given: $(7 x y + 3 x)^{2} - (7 x y - 3 x)^{2}$
We know that,
$(a + b)^{2} = a^{2} + 2 a b + b^{2} (a - b)^{2} = a^{2} - 2 a b + b^{2}$
Subtracting the two,
$(a + b)^{2} - (a - b)^{2} = {a^{2} + 2 a b + b^{2}} - {a^{2} - 2 a b + b^{2}}$
$(a + b)^{2} - (a - b)^{2} = a^{2} + 2 a b + b^{2} - a^{2} + 2 a b - b^{2}$
Grouping the like terms,
$(a + b)^{2} - (a - b)^{2} = 4 a b$

Here, $a = 7 x y$ and $b = 3 x$
So,
$(7 x y + 3 x)^{2} - (4 x y - 3 x)^{2} = 4 (7 x y) (3 x) \Rightarrow (7 x y + 3 x)^{2} - (4 x y - 3 x)^{2} = 84 x^{2} y$

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The value of (7xy+3x)2−(7xy−3x)2 is ____________.

The value of $(7 x y + 3 x)^{2} - (7 x y - 3 x)^{2}$ is ____________.