Problem

Use the binomial theorem to expand each expressio…

02:52

Problem 21 Hard Difficulty

Use the binomial theorem to expand each expression. See Examples 4 and $5 .$
$$
\left(\frac{x}{2}-y\right)^{4}
$$

Answer

$\frac{x^{4}}{16}-\frac{x^{3} y}{2}+\frac{3 x^{2} y^{2}}{2}-2 x y^{3}+y^{4}$

Related Courses

Precalculus

Beginning and Intermediate Algebra

Chapter 14

Sequences and Series

Section 4

The Binomial Theorem

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Video Transcript

Okay, so we want to expand the falling. So let's start with for choose zero. And this is X over two to the power of four, plus a four. Choose one. And then we have X over 23 part three. And then why should a part of one then we have four choose to x over to part two. And then they would have wanted to hurt you. I don't have 4 to 3 and then x over two, and then they provide to the par three. Okay. And then I lost him. That's going to be a four cheese four. And then I got awarded to depart before. Okay, so I would simplify what we have. This isn't one. So we have extra heart for over two seater before, which is 16. Plus, this is a floor, actually, we're gonna have a minus right this time right here. So we have a four over a two to power three, which is bait. So that's just 1/2. So we get X cubed. Why? And then over. It's you and you have four. Choose to Let's for choose to. This is a six, and this is over to depart to which is four. So six over to is or actually 6/4, which is 3/2 to have plus 3/2 on an X squared y squared and unfortunate three. That's a four over to. So that's going to be a minus two, actually, power of one and then watching weaponry. But I do have minus action. That's a plus. Why should before?

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