Question

PLEASE HELP 100 POINTS Consider two integers p and q. Explain why p x (-q) = (-p) x q = -pq.​

Answer 1

I want you to remember this rule:

When multiplying or dividing two different integers that have different signs which are: + (positive sign) and - (negative sign). You get a negative number

However, if you are multiplying or dividing two different integers but they have the same signs. You end up with a positive number

Also multiply are associative, means that they can change the numbers around but they still end up in the same answer

So in this question p x (-q) = (-p) x q = -pq (they put a bracket in the negative number so the question could be easier to be reconize)

We can make:

p = 3

q = 4

So: 3 x -4 = -12

-3 x 4 = -12

-3(4) = -12 (it's a different way to write multiply)

You can see here using the facts that I gave up there supports that

p x (-q) = (-p) x q = -pq

Answer 2

Explanation:

When two variables are together, this means they are supposed to be multiplied. This is why -pq and p x (-q) are equivalent. (-p) x q is the same thing as p x (-q). When two numbers are being multiplied and one is negative, it doesn't matter which one is negative, the ending result will still be a negative number.

I hope you understand what I am trying to say. I explained the best I could, and I hope this helps you. Do well on the test!