Question

Which product is negative

−7⋅(−3)⋅(−9)⋅0
−3⋅4⋅(−2)⋅(−7)
−3⋅5⋅(−6)⋅4
−4⋅(−6)⋅(−3)⋅(−5)

Answer 1

b) −3 ⋅ 4 ⋅ (-2) ⋅ (-7)

Explanation:

Multiplication of positive and negative numbers

• The product of a positive number and a negative number is negative.
• The product of two positive number is positive.
• The product of two negative number is positive.

When we multiply an odd number of negative integers, the negative signs "cancel out" in pairs, leaving one negative sign, thus leading to a negative product.

When we multiply an even number of negative integers, the negative signs again "cancel out" in pairs, but this time they cancel completely, leading to a positive product.

Evaluate each product

`\boxed{(-7) \cdot (-3) \cdot (-9) \cdot 0}`

This product involves a zero, which makes the entire product zero.

`\boxed{(-3) \cdot 4 \cdot (-2) \cdot (-7)}`

This product has an odd number of negative factors (three negative integers), which results in a negative product.

`\boxed{(-3) \cdot 5 \cdot (-6) \cdot 4}`

This product is positive because it has an even number of negative factors (two negative integers), which results in a positive product.

`\boxed{(-4) \cdot (-6) \cdot (-3) \cdot (-5)}`

This product is positive because it has an even number of negative factors (four negatives integers), which results in a positive product.

Summary

In conclusion, the product that is negative is:

`\large\boxed{\boxed{\textsf{b)} \quad -3 \cdot 4 \cdot (-2) \cdot (-7)}}`