Question

Which pair of expressions has the same value?

A. (–2)(–7) and 4 + (–18)
B. (2)(7) and 4 + 18
C. (–2)(7) and 18 + (–4)
D. (2)(–7) and 4 – 18

Answer 1

Option A)

Assuming that (-2)(-7) and 4 + (-18) are equal.

• ⇒ (-2)(-7) = 4 + (-18)

Using the property [-x × -y = x × y = xy]:

• ⇒ (-2)(-7) = 4 + (-18)
• ⇒ (2)(7) = 4 + (-18)

Using the property [x + (-a) = x - a]:

• ⇒ (2)(7) = 4 + (-18)
• ⇒ (2)(7) = 4 - 18
• ⇒ 14 = -14 (False)

Option B)

Assuming that (2)(7) and 4 + 18 are equal.

• ⇒ (2)(7) = 4 + 18
• ⇒ 14 = 22 (False)

Option C)

Assuming that (–2)(7) and 18 + (–4) are equal.

• ⇒ (-2)(7) = 18 + (-4)

Using the property [-x × y = -xy]:

• ⇒ (-2)(7) = 18 + (-4)
• ⇒ (-)(2)(7) = 18 + (-4)
• ⇒ -14 = 18 + (-4)

Using the property [x + (-a) = x - a]:

• ⇒ -14 = 18 + (-4)
• ⇒ -14 = 18 - 4
• ⇒ -14 = 14 (False)

Option D)

Assuming that (2)(-7) and 4 - 18 are equal.

• ⇒ (2)(-7) = 4 - 18

Using the property [-x × y = -xy]:

• ⇒ (-)(2)(7) = 4 - 18
• ⇒ -14 = 4 - 18
• ⇒ -14 = -14 (True)

Therefore, Option D is correct.