Write (4cos2x)(sin4x) as a sum or difference

This is on page 423 of Larson Precalculus with limits
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sin(A+B)=sinAcosB+cosAsinB; sin(A-B)=sinAcosB-cosAsinB.

sin(A+B)+sin(A-B)=2sinAcosB.

Let A=4x and B=2x, A+B=6x, A-B=2x.

Therefore 4cos2xsin4x=2sin6x+2sin2x.
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