Factor 81y^4-18y^2+1

Rewrite y4 as (y2)2.
Let u=y2. Substitute u for all occurrences of y2.
Factor using the perfect square rule.
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Rewrite 81u2 as (9u)2.
Rewrite 1 as 12.
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Rewrite the polynomial.
Factor using the perfect square trinomial rule a2-2ab+b2=(a-b)2, where a=9u and b=1.
Replace all occurrences of u with y2.
Rewrite 9y2 as (3y)2.
Rewrite 1 as 12.
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=3y and b=1.
Apply the product rule to (3y+1)(3y-1).
Factor 81y^4-18y^2+1

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