Which of the following options is not equivalent to the expression $2 (3 x - 3 y)$ ?

6 x - 6 y

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- 6 x + 6 y

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3 (2 x - 2 y)

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5 x - 5 y

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Solution

The correct option is D $5 x - 5 y$
$2 (3 x - 3 y) = (2 \times 3 x) + (2 \times (- 3 y))$
$= 6 x - 6 y$

Option A is equivalent to the expression $2 (3 x - 3 y)$ .

Changing the order does not change the value of the addition, so $6 x - 6 y$ can be written as $- 6 y + 6 x$ .

Option B is also equivalent to the expression $2 (3 x - 3 y)$ .

$3 (2 x - 2 y) = (3 \times 2 x) + (3 \times (- 2 y)) = 6 x - 6 y = 2 (3 x - 3 y)$

Option C is also equivalent to the expression $2 (3 x - 3 y)$ .

In $5 x - 5 y$ , none of the terms matches with $6 x - 6 y$ .
$\Rightarrow 5 x - 5 y and 2 (3 x - 3 y)$ are not equivalent expressions.

Option D is correct.

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