I suspect that what you were told is that on the right-hand side "we can multiply both "top" and "bottom" by -1". This is equivalent, if you think about it, to multiplying by 1 since (-1)/(-1) = 1. And when anything is multiplied by 1 you don't change its value. Hence, the left-hand side remains unchanged when you multiply the right-hand side by 1. (Remember, -1/-1 = 1)Jherek said:Ah. So that explains why the left-hand side is left untouched. It looks like the right hand side has been multiplied by -1 and that is how I've heard it explained before
When simplifying expressions, we often come across a situation where we need to get rid of a negative sign in front of a set of parentheses. In order to do this, we need to multiply the entire set of parentheses by -1. This is because multiplying a negative number by another negative number results in a positive number, effectively cancelling out the negative sign.
The purpose of multiplying by -1 when simplifying is to make the expression easier to work with and understand. By getting rid of negative signs, we can more clearly see the structure and relationships of the terms in the expression, making it easier to manipulate and solve.
Yes, you can always multiply by -1 when simplifying. This is because the distributive property of multiplication allows us to multiply any number by -1 without changing the value of the expression. So, no matter what the terms are in the parentheses, multiplying by -1 will always result in the same simplified expression.
There are two main exceptions to multiplying by -1 when simplifying. The first exception is when the expression already has a negative sign in front of it. In this case, we do not need to multiply by -1 as the negative sign is already accounted for. The second exception is when there is a coefficient or variable outside of the parentheses. In this case, we need to distribute the -1 to all terms inside the parentheses, which may result in a change in the expression.
No, there is no specific order in which you should multiply by -1 when simplifying. As long as you distribute the -1 to all terms inside the parentheses, the order in which you do so does not matter. However, it is important to keep track of any coefficients or variables outside of the parentheses and make sure they are also multiplied by -1 if necessary.