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

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x(y−z)=(x×y)−(x×z)x(y−z)=(x×y)−(x×z)

x(y−z)=(x×y)−zx(y−z)=(x×y)−z

x×(−y)=(−x)×yx×(−y)=(−x)×y

x×(−

\frac{1}{y}

) = (−x)×(

\frac{1}{y}

)

answer is A.

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Detailed Solution

We know that the distributive property of multiplication has two equations, one for addition and one for subtraction
(1) The distributive property of multiplication over addition,
⇒a×(b+c)=(a×b)+(a×c)...... (1)
(2) The distributive property of multiplication over subtraction,
⇒a×(b−c)=(a×b)−(a×c)..... (2)
According to the question, we need to compare (2) with the choices,
Since, the variables are as x, y, and z in the choices,
Put ,
a=x, b=y and c=z in (2), we get
⇒x(y−z)=(x×y)−(x×z) … (3)
x(y−z)=(x×y)−(x×z) shows the distributive property of multiplication over subtraction.
Hence (1) is the correct option.

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