Write the following in the expanded form
$(7 x + y - 5 z)^{2}$

49 x^{2} + y^{2} + 25 z^{2} + 14 x y - 10 y z - 70 z x

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49 x^{2} + y^{2} + 25 z^{2} - 14 x y - 10 y z - 70 z x

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49 x^{2} + y^{2} + 25 z^{2} + 7 x y - 5 y z - 35 z x

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49 x^{2} + y^{2} + 25 z^{2} + 28 x y - 20 y z - 70 z x

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Solution

The correct option is A $49 x^{2} + y^{2} + 25 z^{2} + 14 x y - 10 y z - 70 z x$
We solve the given expression $(7 x + y - 5 z)^{2}$ as shown below:

$(7 x + y - 5 z)^{2}$

$= (7 x)^{2} + (y)^{2} + (- 5 z)^{2} + (2 \times 7 x \times y) + (2 \times y \times (- 5 z)) + (2 \times (- 5 z) \times 7 x)$

$(∵ (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a)$

$= 49 x^{2} + y^{2} + 25 z^{2} + 14 x y - 10 y z - 70 z x$

Hence, $(7 x + y - 5 z)^{2} = 49 x^{2} + y^{2} + 25 z^{2} + 14 x y - 10 y z - 70 z x$ .

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