Question

Which shows two expressions that are equivalent to (-8)(-12)(2)?
A.(-96)(2) and (-8)(-24)

B.(-8)(-24) and (-1)(192)

C.(-96)(2) and (-1)(192)

D.(-8)(-24) and (-16)(-12)

Answer 1

D. is the answer since (-8)(-24)=192 and so does (-16)(-12)

Answer 2

The two expressions that are equivalent to (-8)(-12)(2) are D. (-8)(-24) and (-16)(-12)

Recall the following rules:

$-\times - = +\\- \times + = -\\+ \times + = +$

Applying the above rules, first determine the value of the given expression, (-8)(-12)(2), then find which two expressions has value equivalent to the given expression.

Thus:

$(-8)(-12)(2) = -8 \times -12 \times 2 = 192$

Find which of the options has same value as 192.

Option A:

$(-96)(2) = -96 \times 2 = -192\\(-8)(-24) = -8\times -24 = 192$

One of the expressions of this option is not equivalent to 192, so this is not the answer.

Option B:

$(-8)(-24) = -8 \times -24 = 192\\(-1)(192) = -1 \times 192 = -192$

One of the expressions of this option is not equivalent to 192, so this is not the answer.

Option C:

$(-96)(2) = -96 \times 2 = -192\\(-1)(192) = -1 \times 192 = -192$

Both of the expressions of this option are not equivalent to 192, so this is not the answer.

Option D:

$(-8)(-24) = -8 \times -24 = 192\\(-16)(-12) = -16 \times -12 = 192$

Both of the expressions of this option are equivalent to 192.

Therefore the expressions that are equivalent to (-8)(-12)(2) are D.(-8)(-24) and (-16)(-12).

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