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Perform the indicated operations.

$$(x+1)(x+2)(x+3)$$

$\therefore(x+1)(x+2)(x+3)=x^{3}+6 x^{2}+11 x+6$

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Oregon State University

Harvey Mudd College

University of Nottingham

Boston College

all right, I'm gonna show you how to multiply three by no meals together. And to do this, I'm gonna use the problem. X plus one times X plus two times X plus three. First, we're gonna notice that these are all by no meals because they each have an X in them. They each have a number in them, and all three of them are separated by plus signs. So I like to start with the first to buy no meals and multiply these out. So I'm gonna take this X plus one times this X plus two. And to do that, I'm just gonna do a distributive property where I'm going to take this First x times this X and X Times X would give me an X to the second power X square. I'm going to take the same X times the two in the second binomial. So x times two is Ah, plus two X. I'm not gonna move on to the one in the first binomial one Times X would give me X. And then I'm gonna take the one times the two and get two from here. I'm going to combine any of my terms that are like terms. So this to X and this ex I can combine together and I can actually get a simplified X squared plus three x plus two. So, two x plus, the one ex would give me a three X here. I'm now going to take my X plus three, which was the third binomial, and I'm gonna multiply it to the now try no meal that I have for my first multiple occasions, so I'm writing it in the back. Okay, again, the distributive property. I'll take my X squared times X. So that's X to the third Power X Cube. I'll take the same X squared times three. So that's a plus three x Square. I'm not gonna take the three x Times X, which is another plus three x squared. And then the same three x Times three, which is nine x last the two times X is a plus two x and the two times the three is plus six, right, just like we did with the two by no meals. I can combine anything that or like terms. So I'm gonna underline the two ex Claire terms and the two ex terms Hey, when I can combine the X squared together, I'll get a plus six x squared three plus +36 Keep the X squared plus nine x plus. The two X is 11 x plus the six and this is my final answer to the product of X plus one times X plus two times x plus three