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Current time:0:00Total duration:3:03

Video transcript

luis looked at the expression x minus y times x squared plus XY plus y squared and wrote the following he said using the distributive property so you took X minus y and he I guess he distributed this expression onto the X and this expression onto the negative Y so that's why we have an x times this entire expression over here x times the entire expression minus y times this entire expression then he says using the distributive property again this is equal to so then he distributed this X into that and got all of all of the first the first three terms here he got these first three terms and then he distributed the Y he distributed the Y over here and he got these three terms and then he saw it looks like that this term x squared Y cancels out with the minus x squared Y and the XY squared cancels out with the X negative XY squared and he saw that it equals x to the third minus y to the third and then he wrote down I conjecture that X minus y times x squared plus XY plus y squared is equal to X to the third minus y to the third for all x and y did carlos use inductive reasoning explain well inductive reasoning is looking at a sample of things looking at some set of data if you will and then making a generalization based on that you know you're not 100% sure but based on what you've seen so far you think that the pattern would continue you think it might be true for all things of that have that type of property or whatever now in this situation he didn't look at like some type of a sample he actually just did a proof he multiplied this out algebraically in fact it's incorrect for him to say i conjecture here a conjecture is a statement or proposition that is unproven but it's probably going to be true it's unproven but it seems reasonable or it seems likely that it's true this isn't a conjecture this is proven he proved that X minus y times x squared plus XY plus y squared is equal to X to the third minus y third he should have written and this is a much stronger thing to say he should have said I proved I proved that this is true for all x and y so to answer the question did he use inductive reasoning no I would say that he made an outright proof no he made a proof inductive reasoning would have been if he would have saw you know if you would have given him 5 minus 2 is equal to or 5 minus 2 times 5 squared plus 5 times 2 plus 2 squared and you saw that that was equal to the same thing as 5 to the third minus 2 to the third and then let's say he did it for I don't know 1 & 7 and a couple of examples and it kept holding for all of the examples that was the first number cubed minus the second number cubed then it would been inductive reasoning to say that that is true for all numbers x and y but here it's not an induction is he didn't use induction or I shouldn't say induction he didn't use inductive reasoning he outright proved that this statement this statement is true for all x and y