$(3 x + 4 y + 5 z)^{2}$ = __________________.

9 x^{2} + 16 y^{2} + 25 z^{2} + 24 x y + 40 y z + 30 x z

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9 x^{2} - 16 y^{2} - 25 z^{2} + 24 x y + 40 y z + 30 x z

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4 x^{2} + 25 y^{2} - 16 z^{2} + 32 x y + 24 y z + 30 x z

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16 x^{2} + 9 y^{2} + 64 z^{2} + 42 x y + 24 y z + 12 x z

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Solution

The correct option is A $9 x^{2} + 16 y^{2} + 25 z^{2} + 24 x y + 40 y z + 30 x z$
We know that $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 a c$ .

Here, $a = 3 x, b = 4 y$ and $c = 5 z$ .

On substituting these values in he known identity, we get,
$(3 x + 4 y + 5 z)^{2} = (3 x)^{2} + (4 y)^{2} + (5 z)^{2} + 2 (3 x) (4 y) + 2 (4 y) (5 z) + 2 (3 x) (5 z) = 9 x^{2} + 16 y^{2} + 25 z^{2} + 24 x y + 40 y z + 30 x z$

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Similar questions

(3 x - 4 y + 5 z)^{2}

9 x^{2} + 16 y^{2} + 25 z^{2} - 24 x y - 24 x y - 40 y z + 30 z x

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

3 x^{2} - 2 y^{2} + 5 z^{2} = 0, 7 x^{2} - 3 y^{2} - 15 z^{2} = 0, 5 x - 4 y + 7 z = 6.

9 x^{2} + 24 x y + 16 y^{2} - 25 z^{2}

3 x - 4 y + 2 = 0

(- 2, 3)

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