## anonymous 5 years ago Can (x+a)^2 be broken down into (x-a)(x+a) ?

1. anonymous

no

2. anonymous

Not unless a = 0 $(x+a)^2 = (x-a)(x+a) \rightarrow \frac{(x+a)^2}{(x+a)} = (x-a)$ $\rightarrow x+a = x-a \rightarrow a = -a$

3. anonymous

Okydokey.

4. anonymous

a=0 is the trivial answer. For all x not equal to zero, $(x+a)^{2}=(x+a)(x+a)$

5. anonymous

Sorry, made a typo! I meant for all "a" not equal to zero.

6. anonymous

Ok, I don't know if you're a big fan of integration but I'm sure you'll be able to answer this. If I have the integral of dx / (X^4 - a^4), does that break down into dx / (x-a)^2(x+a)^2 . And then after that using what you've told me, does it break down further into dx / (x-a)(x+a)(x+a)(x+a) ?

7. anonymous

And we're not told what a is equal to.

8. anonymous

let $u = x ^{2}$ then let $b = a ^{2}$ now you have $u^{2}-a ^{2}$ factor out -1 now you have $-(a ^{2}-u ^{2})$ the integral becomes $-1\int\limits du/(a ^{2} - u ^{2})$ Now you can look up the integral in a table of integrals

9. anonymous

made a typo$-(b ^{2}-u ^{2)}$ now the integral becomes $-1 \int\limits du / (b ^{2} - u ^{2} )$ This integral is listed in any table of integrals.