MHB Factor Fourth Degree Expression

[mathdad]

Factor.

x^4 + 2x^2*y^2 + y^4

Must I change x^4 to (x^2)^2 and y^4 to (y^2)^2?

Let u = x^2

Let v = y^2

(u)^2 + 2uv + (v)^2

Where do I go from here?

 

[MarkFL]

Yes, that's a great start...next, observe that that form is the square of a binomial:

$$(a+b)^2=a^2+2ab+b^2$$

 

[mathdad]

Great. I can surely finish now.