Factor 81w^2-u^4w^2

Math
81w2-u4w2
Factor w2 out of 81w2-u4w2.
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Factor w2 out of 81w2.
w2⋅81-u4w2
Factor w2 out of -u4w2.
w2⋅81+w2(-u4)
Factor w2 out of w2⋅81+w2(-u4).
w2(81-u4)
w2(81-u4)
Rewrite 81 as 92.
w2(92-u4)
Rewrite u4 as (u2)2.
w2(92-(u2)2)
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=9 and b=u2.
w2((9+u2)(9-u2))
Factor.
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Simplify.
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Rewrite 9 as 32.
w2((9+u2)(32-u2))
Factor.
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Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=3 and b=u.
w2((9+u2)((3+u)(3-u)))
Remove unnecessary parentheses.
w2((9+u2)(3+u)(3-u))
w2((9+u2)(3+u)(3-u))
w2((9+u2)(3+u)(3-u))
Remove unnecessary parentheses.
w2(9+u2)(3+u)(3-u)
w2(9+u2)(3+u)(3-u)
Factor 81w^2-u^4w^2

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