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CCSS.Math: , ,

Mousa and fateh were each asked to factor the quadratic expression 16x squared minus 64 their responses are shown below so Moosa factored it this way Fatou factored it this way which student wrote an expression that is equivalent to 16 x squared minus 64 so I encourage you to pause the video and figure that out which student wrote an expression that is equivalent to our original one 16x squared minus 64 well let's work through it together so let's see if first we can factor this out somehow to get what Moussa got and it looks like Moussa first factored out a 16 and then he was left with a difference of squares so let's see if we can do that so we can write our original expression 16x squared minus 64 we can write that as 16 times x squared minus 16 times 4 now when you write it like that it's very clear that you can factor out a 16 so this is going to be equal to a 16 times what you have left over is x squared minus 4 and then x squared minus 4 that's the that's a difference of squares right over there so we can that part we can factorize so we have our original 16 and then and then this part right over here we can write as X plus 2 times X minus 2 X plus 2 times X minus 2 if what I just did in this last step going from x squared minus 4 2 X plus 2 times X minus 2 doesn't make any sense I encourage you to watch some of the introductory videos on factoring a difference of squares but the basic idea I have a form here of a squared minus B squared so it's going to have the form of a plus B times a minus B in this case it's x squared minus 2 squared so it's going to be X plus 2 times X minus 2 so that's exactly what Moussa got so this one so Moussa did get an expression that is equivalent to 16 x squared minus 64 now let's think about fatou so fatou didn't factor out a 16 from the get-go it looks like he just immediately recognized that what we our original expression is itself a difference squares even if we don't factor out a 16 and so let's rewrite it so our original expression we could write as so we could write it instead of writing let me just write like this this is our original expression 16x squared minus 64 that's the same thing as 16x squared is the same thing as 4x the whole thing squared and then minus 8 squared so when you write it like this it's clear that this is a difference of squares so this is going to be 4x plus 8 times 4x minus 8 4x plus 8 times 4x minus 8 once again if this last step that I did doesn't make a lot of sense I encourage you to watch the video on factoring difference of squares we be able go a lot more into the intuition of it but when you see it this way you realize that fought 2 also got an expression that is equivalent to 16 x squared minus 64 so they both did