Explain why the product of an integer multiplied by itself cannot be negative.
An integer multiplied by itself is the square of that number.
Each number when squared is positive.
The only number when squaring is negative is √ ( - 1 ) = i
when two numbers of like sign are multiplied, the result is positive.
If you have a positive, positive 6 for example and you multiply it by positive six, that would be a positive.
If you have a negative, negative 14 for example and you multiply it by negative 14, you would also get a positive.
(+) ⋅ (+) = (+)
(-) ⋅ (-) = (-)
Well, imagine you have a negative number, let's say -5. And you want to multiply it by itself, so you do -5 * -5. Now, think about what multiplication really means – it's just repeated addition. When you multiply a positive number by itself, you're basically adding that number to itself multiple times. But what does it mean to add a negative number to itself? It's like trying to take away something from nothing – you can't do it! So, no matter how many times you try to multiply a negative number by itself, you'll never end up with a negative result. It's like trying to make a clown sad – it's just not possible!
To understand why the product of an integer multiplied by itself cannot be negative, let's break it down step by step.
1. Multiplying a positive integer by itself:
When a positive integer is multiplied by itself, the result is always positive. For example, 2 * 2 = 4, 3 * 3 = 9, and so on. This holds true for any positive integer.
2. Multiplying a negative integer by itself:
When a negative integer is multiplied by itself, the result is also positive. For example, (-2) * (-2) = 4, (-3) * (-3) = 9, and so on. When you multiply two negatives, they cancel out and result in a positive value.
3. Combining a positive and negative integer:
If we multiply a positive integer by a negative integer, the result will be negative. For example, 2 * (-3) = -6, 5 * (-4) = -20, and so on.
From the above observations, we can conclude that multiplying two integers with the same sign (either positive or negative) will always result in a positive product. Multiplying an integer with a different sign will produce a negative product.
Therefore, when an integer is multiplied by itself, it will always have the same sign. Since there are no two integers with different signs being multiplied, the product cannot be negative.