Explain why the product of an integer multiplied by itself cannot be negative.
An integer is defined as any whole number from -infinity to infinity.
Therefore, there are three cases
1. The integer is 0
2. The integer is positive
3. The integer is negative
1. If the integer is zero, zero * zero is zero, which is not negative.
2. If the integer is positive, a positive number times a positive number is always a positive number.
3. If the integer is negative, a negative number times a negative number is always a positive number.
An integer is defined as any whole number from -infinity to infinity.
Therefore, there are three cases
1. The integer is 0
2. The integer is positive
3. The integer is negative
1. If the integer is zero, zero * zero is zero, which is not negative.
2. If the integer is positive, a positive number times a positive number is always a positive number.
3. If the integer is negative, a negative number times a negative number is always a positive number.
Well, let me tell you a little joke to explain it. Why did the number 4 never feel negative? Because it was always positive that it would never be negative!
But on a more serious note, let's imagine we have an integer like -6. When we multiply it by itself, we get (-6) x (-6), which is equal to 36. Now, if we had a positive integer, like 6, and multiplied it by itself, we'd also get 6 x 6, which is also 36.
No matter if the number is positive or negative, when you multiply it by itself, you'll always get a positive result because the negative signs cancel each other out. It's like putting two grumpy clowns in a room and expecting them to make each other even grumpier. It just doesn't work! So, the product of an integer multiplied by itself is always positive.
To understand why the product of an integer multiplied by itself cannot be negative, we need to consider the properties of multiplication.
First, let's consider what happens when we multiply two positive integers. When we multiply two positive numbers, such as 3 and 3 (3 * 3), the result is always positive (9 in this case). This is because multiplication is a way of repeating addition. So, multiplying a number by itself is like adding the number to itself repeatedly, which will always result in a positive value.
Similarly, when we multiply two negative numbers, like -3 and -3 (-3 * -3), the result is also positive (9 in this case). This is because multiplying two negatives is essentially flipping the signs twice. So, the double negative cancels out, resulting in a positive value.
Now, if we try to multiply a positive integer by a negative integer, such as 3 and -3 (3 * -3), the result is always negative (-9 in this case). This is because multiplying a positive value by a negative value is essentially flipping the sign once.
However, when we multiply a negative integer by itself, such as -3 and -3 (-3 * -3), the result is always positive (9 in this case). This is because by definition, multiplying a negative value by a negative value results in a positive value.
So, no matter if the integer is positive or negative, when it is multiplied by itself, the product will always be positive. Therefore, the product of an integer multiplied by itself cannot be negative.