Knots and their polynomials
The Calculation of the Jones Polynomial of the Right Trefoil

[t]
=
 t^{1/2}  t^{1/2}.
(Step 3)
 [t]
=
t^{3/2}  t^{1/2} + t^{2}
[t]
(Step 2)
= t^{3/2}  t^{1/2} + t^{2}
( t^{1/2}  t^{1/2})
= t^{5/2}  t^{1/2}.

[t]
=
(t^{3/2}  t^{1/2})
[t] +
t^{2}
(Step 1)
= (t^{3/2}  t^{1/2})
( t^{5/2}  t^{1/2}) +
t^{2}
= t^{4} + t^{3} + t.
This completes the calculation.
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