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Numerade Educator

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Problem 25 Hard Difficulty

Perform the indicated operations.
$$(x-2 y)^{3}$$

Answer

$\therefore(x-2 y)^{3}=x^{3}-6 x^{2} y+12 x y^{2}-8 y^{3}$

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Video Transcript

so we had to expand the equation. X minus two. Why Wanted cute. Now this is equivalent to for those you need to refresh run exponents this sequel into multiplying this three times. So this is equivalent you X minus two. Why? Times X minus two. Why turns next minus two. So next we can break this up into two parts so we can multiply the 1st 2 using the foil method. Then we're going to do that as so. So we get next time backs first. So we get just there, gets X squared. Then we dio x times negative to Why? So we get negative, too. X y and we dio dinners So negative two y turns x Another negative two x y and then we dio last So we do negative two y times negative to mine which will then equal So the negatives become a positive positive four for why squared? It's having a little technical difficulties with McCann. So now we can bring this back to the full equation and right this has X squared minus four. That's why to combine like terms plus more. Why squared since we still have the Met x minus two y At the very end, we still need to remember that and bring that down by as to why So now we can use the distributive property to expand this out further and multiply and the X in the name of two. Why so using the distributive property? We can rewrite this as next times X squared minus four backs. Why? Plus four. Why squared? Minus two. Why Times X squared minus four x y plus four. Why squared so we can expand this? We can start with the X so max times that squared is X cubed Next times negative for X Y is native four X squared. Why waas x times four y squared more next Why squared now? We can also include in the negative Why so negative to why times back squared is negative. Two. That's squared. Why remember you, killer? Because of order of operations of multiplication, The order doesn't matter so you can rearrange your variables and this will come in handy because we can already see that we have a negative for X y in a native to X y so you can combine like terms and seeing the order makes it a lot easier. So now we continue Negative two y times. Negative four x y The negatives will cancel. We're become positive. So we get positive. Eight. That's why Square. It's bad running out a little bit of money. So I'm just going to include it right here. It's a negative two. Y isn't right here. Here. So negative two y times four y squared is negative. Eight. Why cute? So that would go Just, I think there. So now you can combine like terms. Like I said. So we have the X squares wise in that we have X Y squares in gray there so we can simplify this to say x cubed My Iast six x squared y plus four. It was a 12 x y squared minus eight. Why cute? So carrying this down perfect fit it in explains too. Why Huge is equivalent to X cubed minus six x worldwide plus 12 x y squared minus +81 Cute that we get to use be galaxy petting. This is half says and that is our answer. Thank you very much.