Question

Can (x+a)^2 be broken down into (x-a)(x+a) ?

Answer 1

no

Answer 2

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

Answer 3

Okydokey.

Answer 4

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

Answer 5

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

Answer 6

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) ?

Answer 7

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

Answer 8

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

Answer 9

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.