Which of the following shows the distributive property of multiplication over subtraction?

x (y - z) = (x \times y) - (x \times z)

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x (y - z) = (x \times y) - z

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x \times (- y) = (- x) \times y

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x \times (\frac{- 1}{y}) = (- x) \times (\frac{1}{y})

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Solution

The correct option is A $x (y - z) = (x \times y) - (x \times z)$
$x (y - z) = (x \times y) - (x \times z)$ shows the distributive property of multiplication over subtraction.

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{t a n}^{- 1} x + {t a n}^{- 1} y = {t a n}^{- 1} \frac{x + y}{1 - x y}

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= π + {t a n}^{- 1} \frac{x + y}{1 - x y}

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{t a n}^{- 1} \sqrt{{\frac{x (x + y + z)}{y z}}} + {t a n}^{- 1} \sqrt{{\frac{y (x + y + z)}{z x}}} + {t a n}^{- 1} \sqrt{{\frac{z (x + y + z)}{x y}}} =

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x + y + z = x y z

\frac{x + y}{1 - x y} + \frac{y + z}{1 - y z} + \frac{z + x}{1 - z x} = \frac{x + y}{1 - x y} \cdot \frac{y + z}{1 - y z} \cdot \frac{z + x}{1 - z x}

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