MHB Factor Fourth Degree Expression

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To factor the expression x^4 + 2x^2y^2 + y^4, it is helpful to rewrite x^4 as (x^2)^2 and y^4 as (y^2)^2. By substituting u = x^2 and v = y^2, the expression transforms into (u)^2 + 2uv + (v)^2. This form resembles the square of a binomial, specifically (a+b)^2 = a^2 + 2ab + b^2. Therefore, the expression can be factored as (x^2 + y^2)^2.
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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?
 
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Yes, that's a great start...next, observe that that form is the square of a binomial:

$$(a+b)^2=a^2+2ab+b^2$$
 
Great. I can surely finish now.
 

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