5

+2 +1b)y = (x + 2tan x)5...

Question

+2 +1b)y = (x + 2tan x)5

+2 +1 b)y = (x + 2tan x)5



Answers

$$ (x+2)(2 x+1)=?+5 x+2 $$

X plus five times X plus two. Let's use the Rainbow Method So we have X Times X, that's X squared and then we have X times two plus two X X. Now we're done with the axe five. Hence X plus five X and then five times two, which we all know is 10. We're almost done. But when you see two terms the things in between the plus signs that have the same variable to the same power in this case X, you can add them together. So we have two x plus five x that makes seven X you add the coefficients. So our final answer is X squared plus seven x plus 10 titles.

In this problem, let us look at the equation. The question says it is sign five weeks plus. Sign effects should be equal. Stupid Two plus or square of eggs. Well, we see that this stone will always be greater than equal to do. Because the minimum Cossacks value is minimum cost square X value is zero. Similarly, the maximum value that it can take is two. So this is always less than equal. Stupid. One quantity is always ready than equal to do and one quantity is always less than equal to do, which means that both are equal to do so. The only possible case is that signed five x equals to one Sin x equals to one And cossacks equals to zero. The street Solution is should be equals two. Bye Bye. two plus who wanted to buy? This is the solution. That's all.

This problem. Ask us to multiply two by no meals. The terms that were given or X plus five and X minus two. We're going to do this by repeated distribution. So first we're gonna distribute the first by no meal into the second binomial. It will look something like this we will have as a result of that X plus five times eggs. And now I'm gonna do something a little bit different. To keep things straight, I'm gonna change X minus two into X plus Negative two. That's the same thing so that I can keep a plus sign here. And then our second term will be X plus five times negative to the reason I do that is, sometimes when you have a minus sign, it's easy to get confused with the minus Sign goes here or a negative sign goes here, Um, with a plus sign and a negative on the coefficient. It's obvious now what we'll do is the second distribution where we take this this X and bring it back into this binomial. Same thing with this negative too. So doing that, we get X squared plus five x, remember to keep this plus sign here. Plus negative two X plus Negative. Two times five is negative. 10 And now we're almost there. But we just have to simplify and combine like terms. We know that since these have the same base and exponents these air like terms So when we add them together five x plus Negative two x we just get three X So our final answer is gonna be X squared plus three X and I'm gonna change this plus negative back into it minus so X squared plus three X minus 10 and that is our solution.

Say. For problem number 47 we are given X plus five over X minus five plus X minus five over X plus five so they look similar. But we were gonna have to determine what our common denominator is, and we are again going to have to multiply both top and bottom by that opposite denominator. So this side by X minus five and this side by X plus five to establish that common denominator. Now we can't go ahead in just, uh, foil these out, so X plus five times X plus five. That, of course, will give us our X squared plus 10 X plus 25. Now we are adding, so that makes it a little easier. We don't have to keep up with where the negative sign goes, so that would be plus X squared minus 10 X plus 25. And that's all over our common denominator of X plus five times X minus five. So now we can simplify where we can and you should see that 10 x and 10 x Do cancel and we're left with X squared plus X squared, which is two X squared plus 50 over our X plus five times X minus five. Okay, and then that equals because we can factor our numerator now. You could leave it like this if you wanted to, but I like to factor it down as far as it can go. So we can fact around to leaving us with two times X squared plus 25 over our denominator X plus five minus X or excuse me times X minus five. And since none of these convey reduced or factored any further, this is our most simplified expression, and we are finished.


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