### Video Transcript

Determine which of the following expressions has a product of negative 24. Is it A) three multiplied by negative eight, B) three multiplied by eight, C) four multiplied by six, or D) negative four multiplied by negative six?

In this particular question, it is worth firstly considering the factor pairs of 24. These are numbers that multiply or have a product of 24. There are four such pairs, one and 24, two and 12, three and eight, and finally four and six. This means that multiplying three and eight and also four and six gives us an answer of 24. So we cannot rule out any of the options at this stage.

As we’re looking for a product of negative 24, we need to consider what happens when we multiply positive and negative numbers. Multiplying two positive numbers gives us a positive answer. Multiplying a positive and a negative in either order gives us a negative answer. And multiplying two negative numbers gives us a positive answer. If the signs of the two numbers are the same, our answer will be positive, whereas if they’re different, our answer will be negative.

Let’s now consider our four options. Three multiplied by negative eight is equal to negative 24, as we are multiplying a positive by a negative. Options B and C, three multiplied by eight and four multiplied by six, are both equal to 24, as we’re multiplying two positive numbers. Option D also gives us an answer of positive 24, as we’re multiplying negative four by negative six. This means that the correct answer is option A. The expression three multiplied by negative eight has a product of negative 24.