# Algebra question **URL:** \ **Category:** Factual Questions\ **Created:** [February 21, 2005, 3:10pm UTC](https://boards.straightdope.com/t/algebra-question/291177 "2005-02-21T15:10:16Z")\ **Posts on this page:** 14\ **Page:** 1
**Author:** ![dauerbach](https://avatars.discourse-cdn.com/v4/letter/d/c2a13f/32.png) [@dauerbach](https://boards.straightdope.com/u/dauerbach)\ **Post date:** [February 21, 2005, 3:10pm UTC](https://boards.straightdope.com/t/algebra-question/291177/1 "2005-02-21T15:10:16Z")
I’m trying to help my daughter understand algebra. It is sad that she is only in seventh grade and I am have trouble explaining a factoring concept. She is factoring polynomials completely and neither understand how to factor a^4-b^4. I know it has to be simple, and (a-b)^4 certainly is. Any advice? ---
**Author:** ![Malacandra](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@Malacandra](https://boards.straightdope.com/u/Malacandra)\ **Post date:** [February 21, 2005, 3:13pm UTC](https://boards.straightdope.com/t/algebra-question/291177/2 "2005-02-21T15:13:52Z")
(a^2 + b^2) (a^2 - b^2). Time to revise “Difference Of Two Squares”! 🆒 ---
**Author:** ![Grey](https://avatars.discourse-cdn.com/v4/letter/g/b782af/32.png) [@Grey](https://boards.straightdope.com/u/Grey)\ **Post date:** [February 21, 2005, 3:14pm UTC](https://boards.straightdope.com/t/algebra-question/291177/3 "2005-02-21T15:14:36Z")
What would you do if you replaced the [sup]4[/sup] with [sup]2[/sup]? Since the powers are even you should be able to extrapolate from there. ---
**Author:** ![SandWriter](https://avatars.discourse-cdn.com/v4/letter/s/8491ac/32.png) [@SandWriter](https://boards.straightdope.com/u/SandWriter)\ **Post date:** [February 21, 2005, 3:35pm UTC](https://boards.straightdope.com/t/algebra-question/291177/4 "2005-02-21T15:35:36Z")
> [@dauerbach](#): > > Any advice? You can also check out [www.mathforum.org](http://www.mathforum.org). I found that site when I was looking up an equation. It has a lot of cool stuff, including an excellent refresher on probability. Now you can stay one step ahead. ---
**Author:** ![dauerbach](https://avatars.discourse-cdn.com/v4/letter/d/c2a13f/32.png) [@dauerbach](https://boards.straightdope.com/u/dauerbach)\ **Post date:** [February 21, 2005, 5:25pm UTC](https://boards.straightdope.com/t/algebra-question/291177/5 "2005-02-21T17:25:59Z")
Well, that was ridiculously easy. The second set of problems I am having trouble understanding and therefore explaining is clearly the difference of squares in a different form. Examples are (a+b)^2-(a-c)^2 or a(a^2-9)-2(a+3)^2. The answers I get are just not correct. What process do you use to do this. Is there a different website where such questions are more acceptable? ---
**Author:** ![Monstre](https://avatars.discourse-cdn.com/v4/letter/m/e274bd/32.png) [@Monstre](https://boards.straightdope.com/u/Monstre)\ **Post date:** [February 21, 2005, 5:57pm UTC](https://boards.straightdope.com/t/algebra-question/291177/6 "2005-02-21T17:57:15Z")
Well, part of it is just a matter of looking for the appropriate patterns. For example, in this one, the difference of two squares appears in the bolded part: a\*\*(a^2-9)\*\*-2(a+3)^2 and this becomes: a\*\*(a-3)(a+3)\*\* - 2(a+3)^2 Noticing that there’s the factor (a+3) in both terms (each side of the subtraction), you can pull that out, and get: a(a-3) - 2(a+3) Now expand the part in the brackets and you’ll have a standard-looking polynomial to factor. Whole thing will come out to three roots. ---
**Author:** ![dauerbach](https://avatars.discourse-cdn.com/v4/letter/d/c2a13f/32.png) [@dauerbach](https://boards.straightdope.com/u/dauerbach)\ **Post date:** [February 21, 2005, 8:32pm UTC](https://boards.straightdope.com/t/algebra-question/291177/7 "2005-02-21T20:32:37Z")
Thanks, but still can’t get (a+b)^2-(a-c)^2. Anyone want to help me out and make me feel dumb? ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [February 21, 2005, 9:18pm UTC](https://boards.straightdope.com/t/algebra-question/291177/8 "2005-02-21T21:18:16Z")
> [@dauerbach](#): > > Thanks, but still can’t get (a+b)^2-(a-c)^2. Anyone want to help me out and make me feel dumb? It’s still a difference of squares: (a + b)[sup]2[/sup] - (a - c)[sup]2[/sup] = ((a + b) - (a - c))((a + b) + (a - c)). I’ll let you simplify. ---
**Author:** ![TJdude825](https://avatars.discourse-cdn.com/v4/letter/t/dec6dc/32.png) [@TJdude825](https://boards.straightdope.com/u/TJdude825)\ **Post date:** [February 22, 2005, 12:59am UTC](https://boards.straightdope.com/t/algebra-question/291177/9 "2005-02-22T00:59:51Z")
> [@Malacandra](#): > > (a^2 + b^2) (a^2 - b^2). Time to revise “Difference Of Two Squares”! 🆒 Most teachers I’ve had would give half credit for this. Now you have another difference of squares, so you get: a^4 - b^4 (a^2 + b^2)(a^2 - b^2) (a^2 + b^2)(a + b)(a - b) ---
**Author:** ![chaoticbear](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@chaoticbear](https://boards.straightdope.com/u/chaoticbear)\ **Post date:** [February 22, 2005, 2:46am UTC](https://boards.straightdope.com/t/algebra-question/291177/10 "2005-02-22T02:46:54Z")
Has she learned about _i_ yet? I only ask because apparently my 7th grade algebra learned about it on accident, as the result of a too-curious 11-year-old. If so, I’d like to be the first to chime in that (a[sup]2[/sup]+b[sup]2[/sup])=(a+b_i_)(a-b_i_) 🆒 ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [February 22, 2005, 2:49am UTC](https://boards.straightdope.com/t/algebra-question/291177/11 "2005-02-22T02:49:39Z")
> [@chaoticdonkey](#): > > Has she learned about _i_ yet? I only ask because apparently my 7th grade algebra learned about it on accident, as the result of a too-curious 11-year-old. > > If so, I’d like to be the first to chime in that > (a[sup]2[/sup]+b[sup]2[/sup])=(a+b_i_)(a-b_i_) 🆒 a[sup]2[/sup] + b[sup]2[/sup] is only factorable if you’re asked to factor over **C**. If you’re asked to factor over **R** (which most 7th-grade math homework would do), the correct answer is that a[sup]2[/sup] + b[sup]2[/sup] is irreducible (i.e., not factorable). ---
**Author:** ![Omphaloskeptic](https://avatars.discourse-cdn.com/v4/letter/o/bcef8e/32.png) [@Omphaloskeptic](https://boards.straightdope.com/u/Omphaloskeptic)\ **Post date:** [February 22, 2005, 3:03am UTC](https://boards.straightdope.com/t/algebra-question/291177/12 "2005-02-22T03:03:16Z")
> [@ultrafilter](#): > > a[sup]2[/sup] + b[sup]2[/sup] is only factorable if you’re asked to factor over **C**. If you’re asked to factor over **R** (which most 7th-grade math homework would do), the correct answer is that a[sup]2[/sup] + b[sup]2[/sup] is irreducible (i.e., not factorable). Now a[sup]4[/sup] + b[sup]4[/sup], on the other hand… ---
**Author:** ![Malacandra](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@Malacandra](https://boards.straightdope.com/u/Malacandra)\ **Post date:** [February 22, 2005, 12:53pm UTC](https://boards.straightdope.com/t/algebra-question/291177/13 "2005-02-22T12:53:39Z")
> [@TJdude825](#): > > Most teachers I’ve had would give half credit for this. Now you have another difference of squares, so you get: > > a^4 - b^4 > (a^2 + b^2)(a^2 - b^2) > (a^2 + b^2)(a + b)(a - b) Most teachers I’ve had would give you part of the answer and let you finish off 😛 > [@Omphaloskeptic](#): > > Now a[sup]4[/sup] + b[sup]4[/sup] on the other hand… Yup. (a^2 + sqrt(ab) + b^2)(a^2 - sqrt(ab) + b^2). And hence with a little application we can factor a^8 - b^8 😃 ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [February 22, 2005, 3:47pm UTC](https://boards.straightdope.com/t/algebra-question/291177/14 "2005-02-22T15:47:05Z")
> [@dauerbach](#): > > I’m trying to help my daughter understand algebra. It is sad that she is only in seventh grade and I am have trouble explaining a factoring concept. She is factoring polynomials completely and neither understand how to factor a^4-b^4. I know it has to be simple, and (a-b)^4 certainly is. Any advice? First of all, if you think those two are the same, you’re drastically mistaken (unless you’re working over a field of characteristic 2). Anyhow, this looks like a classic example of “difference of squares”. A lot of high school algebra techniques are special tricks and you really don’t want to know the deep ideas. Hell, _I_ don’t really fully grok the deep ideas. In general, this trick is that (x+y)(x-y) = x[sup]2[/sup]-y[sup]2[/sup]. Multiply it out to check. Apply it first to x = a[sup]2[/sup] and y = b[sup]2[/sup]. Then look for other differences of squares in the result.