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Structure in expressions — Basic example

Video transcript

- [Instructor] Which of the following is equivalent to the above expression? So they have p plus one squared minus four, and then I have all these choices. P plus one plus two times p plus one minus two. P minus one plus two times p minus one minus two. And so in, these kind of are reminiscent of difference of squares, and when you look at this right over here, this is indeed a difference of squares. We could rewrite this one as, this is the same thing as p plus one squared minus two squared, this literally is a difference of squares. And you might remember from your algebra if I have a squared minus b squared, this can be factored out as a plus b times a minus b. So we could do the same thing over here. This thing is going to be, and we're not used to treating a expression like p plus one as our a, but there's no reason why we can't. This is going to be equal to, and let me color code it. This is going to be, actually, let me, so it's gonna be the product of two things. It's going to be the product of two things. So it's going to be p plus one, so p plus one here, p plus one here. And then plus b and minus b. In this case, b, in this case, b is two. So plus two and then minus two. Once again, this is just a difference of squares, and encourage you to search for difference of squares on Khan Academy if this is looking completely foreign to you. This is a kind of an interesting variation on it. But let's see which ones, this is actually fully described by this one right over here. Do that in a appropriate color, all right. P plus one plus two times p plus one minus two. Yup, that one right there.