Find the cube of 3x - 2y - 4z

27 x^{3} - 54 x^{2} y + 36 x y^{2} - 8 y^{3} - 108 x^{2} z + 144 x y z - 48 y^{2} z + 144 x z^{2} - 96 y z^{2} - 64 z^{3}

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81 x^{3} - 54 x^{2} y + 36 x y^{2} - 8 y^{3} - 108 x^{2} z + 144 x y z - 48 y^{2} z + 169 x z^{2} - 96 y z^{2} - 27 z^{3}

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81 x^{3} + 54 x^{2} y + 36 x y^{2} - 8 y^{3} - 108 x^{2} z + 27 x y z - 48 y^{2} z + 169 x z^{2} - 96 y z^{2} - 27 z^{3}

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27 x^{3} + 54 x^{2} y + 36 x y^{2} + 8 y^{3} + 108 x^{2} z + 144 x y z - 48 y^{2} z + 144 x z^{2} - 96 y z^{2} - 64 z^{3}

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Solution

The correct option is A $27 x^{3} - 54 x^{2} y + 36 x y^{2} - 8 y^{3} - 108 x^{2} z + 144 x y z - 48 y^{2} z + 144 x z^{2} - 96 y z^{2} - 64 z^{3}$
$(a + b)^{3} = a^{3} + b^{3} + 3 a b (a + b)$

So if a=3x-2y and b=-4z we get

$(3 x - 2 y)^{3} - 12 z (3 x - 2 y)^{2} + 48 z^{2} (3 x - 2 y) - 64 z^{3}$

$(3 x - 2 y)^{3} = 27 x^{3} - 54 x^{2} y + 36 x y^{2} - 8 y^{3} a n d (3 x - 2 y)^{2} = 9 x^{2} - 12 x y + 4 y^{2}$

$∴ (3 x - 2 y - 4 z)^{3} = 27 x^{3} - 54 x^{2} y + 36 x y^{2} - 8 y^{3} - 108 x^{2} z + 144 x y z - 48 y^{2} z + 144 x z^{2} - 96 y z^{2} - 64 z^{3}$ .

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