Please help me understand where this expansion came from

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SUMMARY

The discussion centers on the algebraic manipulation of the expression (asinz + bsin3z)^3, specifically focusing on the application of trigonometric identities and algebraic techniques to simplify the equation. The transformation utilizes basic algebra and trigonometric identities to express the equation solely in terms of sin z and sin 3z. Participants clarify that advanced methods like Taylor series or binomial expansion are not necessary for this simplification, emphasizing the straightforward nature of the algebra involved.

PREREQUISITES
  • Understanding of trigonometric identities
  • Basic algebraic manipulation skills
  • Familiarity with polynomial expansion
  • Knowledge of sine functions and their properties
NEXT STEPS
  • Review trigonometric identities for sine functions
  • Study polynomial expansion techniques
  • Explore algebraic manipulation strategies
  • Learn about the applications of Taylor series in trigonometry
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Students studying algebra and trigonometry, educators teaching mathematical concepts, and anyone looking to enhance their understanding of polynomial expressions involving trigonometric functions.

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Homework Statement



(asinz + bsin3z)^3 = (3a/4)(a^2 – ab + 2b^2)sinz – (1/4)(a^3 – 6a^2 – 3b^3)sin3z...

Homework Equations





The Attempt at a Solution



How is this so !? What is being used here (taylor/binomial...?)
 
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Nothing that exotic. It's just algebra and the application of trig identities to get everything in terms of just sin z and sin 3z.
 

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