Not a homework problem, just something I came across in my book that makes sense but not fully.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Factor: ##a^4-b^4##

2. Relevant equations

3. The attempt at a solution

The book's solution:

##a^4-b^4##

##=a^4-a^3b+a^3b-a^2b^2+a^2b^2-ab^3+ab^3-b^4##

##=a^3\left(a-b\right)+a^2b\left(a-b\right)+ab^2\left(a-b\right)+b^3\left(a-b\right)##

##=\left(a-b\right)\left(a^3+a^2b+ab^2+b^3\right)##

Just what is going on here? Such a tiny binomial resulting in something way larger, with what seem like arbitrary terms added in.

Additionally, it gives another factorization of the given problem ##a^4-b^4## which is also factored into ##\left(a^2-b^2\right)\left(a^2+b^2\right)##

You can have more than one correct solution when factoring a polynomial? In what situations would one be the "correct vs incorrect" way? Or is it synonymous with something like factoring 12 into 4*3, 6*2, 12*1 where they are all correct?

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# Homework Help: Adding "annihilating terms" to factor

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