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Factor the following as if it were a trinomial.

25x^(3/2) + 10x^(3/4) + 1

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let y = 5^(3/4) then your expression becomes

( (5x)^(3/4) )^2 + 2(5^(3/4) + 1
= y^2 + 2y + 1
= (y + 1)^2

= ( 5x^(3/4) + 1)^2

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