1. ## Intermediate algebra

Can't really understand how to do this one guys. x2 - 18x + 81 - 16y2 supposedly you start grouping and making a perfect square​ trinomial. if someone can give me a detailed rundown on how best to solve this I'd be very grateful.

2. ## Re: Intermediate algebra

Originally Posted by Saxon
Can't really understand how to do this one guys. x2 - 18x + 81 - 16y2 supposedly you start grouping and making a perfect square​ trinomial. if someone can give me a detailed rundown on how best to solve this I'd be very grateful.
$\displaystyle x^2 - 18x + 81 - 16y^2 = (x^2 - 18x + 81) - 16y^2 = (x - 9)^2 - 16y^2$

This is the difference of two squares. Can you finish?

-Dan

3. ## Re: Intermediate algebra

No, this is where I get lost. I know the formula is supposed to be A2-2AB+B2=(A-B)2 but I'm not sure what goes where and how to figure it out.
then the next step is A2-B2=(A+B)(A-B) which gives the answer (x-9+4y)(x-9-4y) but how can there be 3 terms like that? I'm pretty lost.

4. ## Re: Intermediate algebra

Originally Posted by Saxon
No, this is where I get lost. I know the formula is supposed to be A2-2AB+B2=(A-B)2 but I'm not sure what goes where and how to figure it out.
then the next step is A2-B2=(A+B)(A-B) which gives the answer (x-9+4y)(x-9-4y) but how can there be 3 terms like that? I'm pretty lost.
$(x - 9)^2 - 16y^2=[(x-9)-4y]\cdot[(x-9)+4y]$
That is the answer, period. That is the most simple mathematics.

5. ## Re: Intermediate algebra

Yes you are right it is. I'm not disputing that at all. I'm merely looking for an understanding on how the formulas are applied to the equation to get the answer. If you were to present another similar equation I would be unable to solve it using the formulas as I don't know how to apply them.

6. ## Re: Intermediate algebra

Originally Posted by Saxon
Yes you are right it is. I'm not disputing that at all. I'm merely looking for an understanding on how the formulas are applied to the equation to get the answer. If you were to present another similar equation I would be unable to solve it using the formulas as I don't know how to apply them.
My advice is for you the forget needing formulas for every question.
Now that is not to say that there are not some formulas that are useful: the difference of squares; the square of a binomial; the general binomial.
But if you do fifty or more examples the overall idea will become clear to you.
But again, it is a gross mistake to look for a formula before trying to first see how the terms relate to one another.

7. ## Re: Intermediate algebra

That is a good point. I can see what you mean. For this type of problem I guess I need an in depth and detailed explanation on how this works. I usually use youtube videos to learn this stuff when I find the textbook lacking. But with this one I'm not even sure what to search for. I tried factoring polynomials by grouping but I can't find this type of stuff.

8. ## Re: Intermediate algebra

$x-9$ is just a value. It is one term. If I plug in $x=9$ it is the value 0. So, you have $(x-9)^2-(4y)^2$ is the difference of two squares. If it helps you to think about it, you can use the substitutions: $A=x-9,B=4y$ then apply the formula. Once you apply the formula, substitute back.

9. ## Re: Intermediate algebra

Originally Posted by Saxon
Can't really understand how to do this one guys. x2 - 18x + 81 - 16y2 supposedly you start grouping and making a perfect square​ trinomial. if someone can give me a detailed rundown on how best to solve this I'd be very grateful.
What are you trying to solve for? Your expression is mot an equation so you can't solve for X and Y! Even if it was an equation, you still can't solve for X and Y because you need two equations to silve for two variables.

Steve

10. ## Re: Intermediate algebra

I don't think Saxon mean "solve" in that sense (which is, of course, the technically correct sense). He just mean "do this problem".