Factor y^(3m)-1

Math
y3m-1
Rewrite y3m as (ym)3.
(ym)3-1
Rewrite 1 as 13.
(ym)3-13
Since both terms are perfect cubes, factor using the difference of cubes formula, a3-b3=(a-b)(a2+ab+b2) where a=ym and b=1.
(ym-1)((ym)2+ym⋅1+12)
Simplify.
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Multiply the exponents in (ym)2.
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Apply the power rule and multiply exponents, (am)n=amn.
(ym-1)(ym⋅2+ym⋅1+12)
Move 2 to the left of m.
(ym-1)(y2m+ym⋅1+12)
(ym-1)(y2m+ym⋅1+12)
Multiply ym by 1.
(ym-1)(y2m+ym+12)
One to any power is one.
(ym-1)(y2m+ym+1)
(ym-1)(y2m+ym+1)
Factor y^(3m)-1

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