At 2:10, you have mn = n^2. At this point you should be done. If n = 0, m can be anything and the equation is true. If n is not 0, divide both sides by n, and you have m = n. So your solution space is two lines: n = 0 and n = m. At this point I'm concerned how you could pad this to make a 15-minute video, since you should be done by 2:30.
There's a mistake in this solution. You state that because 0 = 0, that means that they're both equal to 0. That's not exactly true. 0 = 0 is always a true statement, so that tells us nothing about it. For instance, let's take a look at if M = 5, and N = 5. That would mean that in our original equation, we have (5 - 5)^2 = 5^2 - 5^2, which means that 0^2 = 25 - 25, and then 0 = 0, therefore true. So, our solutions are either N = 0, or M = N, both of those do not need to be true at the same time for our equation to work. So, either N = 0, and M is undefined. Or M = N, and any value of M or N will work. You also forgot when dividing that is undefined when m = n, because m - n = 0, and you can't divide by 0. So our solutions are n = 0, and m is undefined. Or m = n, and both are undefined. m does not have to be 0.
At 2:10, you have mn = n^2. At this point you should be done. If n = 0, m can be anything and the equation is true. If n is not 0, divide both sides by n, and you have m = n. So your solution space is two lines: n = 0 and n = m. At this point I'm concerned how you could pad this to make a 15-minute video, since you should be done by 2:30.
There's a mistake in this solution. You state that because 0 = 0, that means that they're both equal to 0. That's not exactly true. 0 = 0 is always a true statement, so that tells us nothing about it. For instance, let's take a look at if M = 5, and N = 5. That would mean that in our original equation, we have (5 - 5)^2 = 5^2 - 5^2, which means that 0^2 = 25 - 25, and then 0 = 0, therefore true. So, our solutions are either N = 0, or M = N, both of those do not need to be true at the same time for our equation to work. So, either N = 0, and M is undefined. Or M = N, and any value of M or N will work. You also forgot when dividing that is undefined when m = n, because m - n = 0, and you can't divide by 0. So our solutions are n = 0, and m is undefined. Or m = n, and both are undefined. m does not have to be 0.
either n=0 or m=n
I found this to be pretty easy... m=n, doesn't matter what the values are as long as that is the case
Or n =0.