Simplify:

Question

Simplify:

2 (x + h)^{2} + 3 (x + h) + 5 - (2 x^{2} + 3 x + 5)

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Accepted Answer

Welcome back. I'm so glad you're here. We are given a function. The function is F of X equals X squared plus X plus one. And we're asked to solve for this here, F of X plus H minus F of X divided by H. So I'm going to rewrite this and I'm going to color code it a little bit. So for the first one we're going to have F of X plus H and we're going to need to do a little bit of work to get that minus F of X and that's the one we're given already. So put that in purple, all divided by H. So let's work on the X plus H. I'm going to copy down our given F of X equals X squared plus X plus one. And what we're looking for is F of X plus H equals And that means for F of X plus H. Whenever there was an X in the original equation, we're going to replace it with X plus H. So instead of X squared it's X plus H squared and instead of plus X it's plus X plus H And bring down our plus one. Okay, for X plus H square that's going to be parentheses, X plus H times parentheses X plus H plus X plus H, N plus one. Let's go ahead and foil this out. We've got X times X. That's going to be X squared. Our outsides X times H is plus X H R insides H times X is plus X. H and R. Last H times H is plus H squared. Bring down our plus X. R. Plus H. And R. Plus one. We can combine like terms there actually aren't that many. We've got our two X. H. Is here. So that'll be X squared plus two X. H plus H squared plus X plus H plus one awesome. Now we have everything that needs to be plugged in to our original expression here. So I'll rewrite this long thing up here for F. Of X plus H. That's the same as X squared plus two X. H plus H squared plus X plus H plus one minus this F. Of X. Which is the same as X squared plus X plus one. All divided by H. Now for the next step let's take this negative and will distribute it to all three terms inside the parentheses. So bringing down this long thing X squared plus two X H plus H squared plus X plus H plus one minus X squared minus x minus one. All. Still divided by this lonely H. Now let's look for like terms, let's look at the purple ones. See if they have a match in the blue. Well negative X squared and a positive X squared. That's zero a negative X. Well here's a positive X. That's zero a negative one. There's a positive one that's zero. Great. Now what have we got left? We've got two X. H plus H squared plus H. All divided by H. We'll look at all three terms in the numerator. They all have an H. So let's factor out and H. So that will leave us with H. Times two X plus H plus one, all divided by H. And look at that. Those Hs cancel out. So what we have left we've got two X plus H plus one and that is as simplified as that's going to get me rewrite that. We look at our answer choices and just moving things around a little bit that matches with answer choice. B. Well done, we'll catch you on the next one.

Simplify: $2 (x + h)^{2} + 3 (x + h) + 5 - (2 x^{2} + 3 x + 5)$ .

Key Concepts

Polynomial Expansion

Combining Like Terms

Distributive Property

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