small math problem

ericf19931

Daemon Poster
Messages
671
i have a small math problem that i dont get. its a^4-2a^2+1 your suppose to factor that completely. the answer is (a+1)(a+1)(a-1)(a-1) but i dont know how that is. can anyone show me a step by step on how to solve this?
 
hmm... I haven't done this in awhile but I don't think that (a+1)(a+1)(a-1)(a-1) is the right answer.

The problem: a^4-2a^2+1 is easy to factor. All you do is find what the powers have in common. They both have a power of 2, so you'd factor out A^2.
After A^2 is factored out, you'd get A^2(A^2 -2 + 1) and then you solve -2+1 and that's it. I'm kinda tired and I'm not sure that's completely right since it's been awhile since I've done factoring, but I think that's how to do it.
 
No, I'm pretty sure that's wrong troy because you can't pull a² out of 1.

I'm not sure how to do it...I think you'd have to pull out a², which gets you a²(a²-2)+1...but that doesn't factor any farther.
 
No, I'm pretty sure that's wrong troy because you can't pull a² out of 1.

I'm not sure how to do it...I think you'd have to pull out a², which gets you a²(a²-2)+1...but that doesn't factor any farther.

how do you type exponents?
 
No, I'm pretty sure that's wrong troy because you can't pull a² out of 1.

I'm not sure how to do it...I think you'd have to pull out a², which gets you a²(a²-2)+1...but that doesn't factor any farther.

Yeah you're right. Like I said, it's been awhile since I've done this. I haven't done algebra in awhile, but hey it doesn't hurt to give it a shot right? :) Sorry I can't help more... boy it's amazing how quick algebra leaves your mind. It's been about a year since I had this stuff and I've already forgotten a lot of it.

ericf1993,
I'd like to know how to type exponents too. I always use the carrot ^ but that gets confusing sometimes.
 
Haha yeah, don't worry about it..

@eric - I used the character map:
- Start
- Program Files
- Accessories
- System Tools
- Character Map


I got this from some website:
Simplifying
a^4 + -2a^2 + 1

Reorder the terms:
1 + -2a^2 + a^4

Factor a trinomial.
(1 + -1a^2)(1 + -1a^2)

Factor a difference between two squares.
((1 + a)(1 + -1^a))(1 + -1a^2)

Factor a difference between two squares.
((1 + a)(1 + -1a))(1 + a)(1 + -1a)

Final result:
(1 + a)(1 + -1a)(1 + a)(1 + -1a)
 
Back
Top Bottom