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# Multiplying positive & negative numbers

Learn some rules of thumb for multiplying positive and negative numbers. Created by Sal Khan.

## Want to join the conversation?

• what would -5 x 1 be? 1 x any other number is that number but i do not know if that works for negatives.
• Yes, it works for negatives, too. 1 is a pretty cool number.
• what happens if you have a negative times a positive times a positive or a negative times a negative times a positive?
• Good question. A negative times a negative times a positive will be a positive⏤the first two negatives cancel each other out to make a positive, so when you multiply them by a positive you will be multiplying a positive times a positive. Likewise a negative times a positive times a positive⏤the first two (neg. times pos.) will make a negative so when you multiply that by another positive you will end up with a negative. Does this make sense?
• Would two negatives being multiplied the same thing as thinking there both positive? Example: -a*-b = a*b true or false?
• stan is absolutely right, if you multiply or divide any two negative numbers, the answer will be positive. so yes your example is true. if you still cant figure it out, try to find a lesson about multiplying and dividing positive and negative integers
• Why is negative times a negative a positive while positive times a positive is not negative?
• A simpler algebraic proof
Using the fact multiplication is commutative, a negative times a positive is also negative. Similarly, we can prove that a negative times a negative is a positive. Since we know that −ab is negative, and the sum of these two terms is 0, therefore (−a) × (−b) is positive
• `What is going on in the comments?`
• What’s going on is that people are just posting random things and being annoying
• If a=2

And the problem I'm solving for is -2^a

Then is this problem supposed to look like -(2 x 2) or (-2) (-2)?
I'm so confused.
• If 'a' is a positive 2 and we have a negative 2 we are multiplying it as -2 x 2 which also looks like -(2 x 2). If you had two negative numbers your example would be (-2)(-2).
• how to solve binomeals
Here's how to solve them:

For example, lets have the straight-up maths question (x + 7) (x + 12).
First, you multiply the two unknowns into x^2, then you multiply the first 'x' with the '+12', turning it into '12x'. After that, you multiply the '+7' with the unknown in the second set of brackets, making it '7x', and finally, you multiply the '+7' with the '+12', making 84.

But we're not done yet. You now need to chuck them all into an equation. So, the x^2' comes first, then the '+12x', then the '7x', then the '84', so the equation is as follows:
(x + 7) (x + 12) = x^2 + 12x + 7x + 84.
Of course, you can simplify it (slightly). Combine the only set of like terms, and voilà! Your equation turns into x^2 +19x +84. Pretty simple, innit?

Sadly, life has its ups and downs, or should I say positives and negatives? It's the same with maths, or binomials, in our case. Here's another question:

(x + 4) (2x - 6)
Oh! what's that? It's a wild minus sign! (I really need to get friends...). You may have noticed that in the previous question, I put the respective signs in front of their respective numbers, regardless of if they're positive or negative. That helps me (and possibly you) distinguish the sign of them and not get jumbled up between the mind-boggling positives and negatives. Now, onto the question. It's the same procedure as before, but now with an extra challenge - the negative sign, the step-by-step is as follows:
2x x x = +2x^2
-6 x x = -6x
4 x 2x = +8x
-6 x 4 = -24
Now to get them into the equation: (x + 4) (2x - 6) = 2x^2 - 6x + 8x -24, which simplifies to 2x^2 + 2x - 24.

You also might come across some specials ones like (x + 3)^2, which if they are all represented in unknows, equals to a^2 + ab (a x b) + ab + b^2, which simplifies to a^2 + 2ab + b^2. In the opposite case, however, like (x - 3)^2, it's literally the same thing but instead of the second addition symbol in the simplified version, it's a subtraction symbol instead. You might be wondering, 'why isn't the last addition symbol negative as well?' Well, allow me to explain. With binomials, at the end of the equation with the two numbers, you multiply them together. But if the binomial is a duplicate of each other, you just square the last number, and put it in the equation, and their sign will always be positive (unlike me) because two positives make a positive, while two negatives also make a positive. Keep in mind that this only works for 'squared' binomials.

Here's another special example of a binomial - (x + 6) (x - 6). This marvellous binomial is nicknamed 'the difference of two squares', and once you memorise the formula, it's really a cake walk to do these types of questions. (a + b) (a - b) = a^2 - ab + ab - b^2. The two 'ab's cancel each other out, so you're left with the first number's square minus the second number's square.

That's the end of my hopefully educational and fun lecture, and I hope anyone who reads this has a wonderful week. Please consider upvoting as this took me half an hour to make, and thank you for staying this long to read what I have to say about binomials! I live in Australia by the way, so some of my spellings may be different from the rest of you.
• If you multiply six positive numbers,the products sign will be ?
• If there are an even amount of negatives, it's positive, if there are an odd amount of negatives, it's negative.
• how would we multiply fractions