 In this video, we present the solution to question number seven from practice exam number three from math 1050, in which case we have to expand the binomial 2x plus 1 to the fourth power. So the easiest way to do this is actually use the binomial theorem that does require Pascal's triangle for which we need the fourth row. So 1, 3, 3, 1, and now let X only need 1, 4, 6, 4, 1. So these right here are the binomial coefficients we need in our expansion. So as we multiply this thing out, we're going to have 2x to the fourth times 1. So you get 1 times 2 to the fourth times x to the fourth. The next one here, you're going to get 4 times 2 cubed x cubed. Next, we're going to get 6 times 2 squared x squared. Come down to the next line right here. We're going to get 4 times 2 to the first x. And then lastly, we've got 1 times, well, 2 to the 0x to the 0. Let's just be a 1. So simplifying these things, 2 to the fourth is 16. So you get 16x to the fourth. Let's see, 2 cubed is 8 times that by 4 is going to give you 32, 32x cubed. The next one here, you have 2 squared, which is 4 times 6 is 24, 24x squared. Next, we have 4 times 2, which is 8 and you get an 8x and you get a plus 1. And so that would be the expanded form looking amongst the answers. We see that is exactly choice C, which then must be the correct answer.