How do I factorise this radian equation?

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Discussion Overview

The discussion revolves around the factorization of the trigonometric expression 2sinx cosx - 4sin^3x cosx. Participants are seeking a detailed breakdown of the mathematical steps involved in the factorization process, with an emphasis on understanding rather than simply obtaining an answer.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant requests a full explanation of every mathematical step involved in factorizing the expression.
  • Another participant points out the common factors in the terms and emphasizes the need for the original poster to show their work to receive help.
  • A third participant questions whether this is a repeat post of the same problem, indicating potential redundancy in the discussion.
  • One participant suggests that the factorization can be approached similarly to a simpler algebraic expression, urging the original poster to demonstrate their algebra skills.
  • Another participant insists that the original poster must provide initial steps before receiving further assistance, indicating a preference for collaborative problem-solving.
  • One participant outlines a series of steps for factorization, including substituting trigonometric functions and applying known identities, while encouraging the original poster to engage with the problem.

Areas of Agreement / Disagreement

Participants generally agree on the need for the original poster to show their work and engage with the problem. However, there is no consensus on the best approach to factorization, and the discussion remains somewhat unresolved regarding the specific steps to take.

Contextual Notes

There are indications that some participants believe this problem may have been previously discussed, which could affect the context of the current inquiry. Additionally, the discussion reflects a tension between providing help and adhering to forum rules regarding homework assistance.

Olly_price
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Factorise:

2sinx cosx - 4sin^3x cosx

I don't want just a simple explanation with an answer, I need a full explanation of every mathematical step.
 
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2 * S * C - 4 * S * S * S * C

cant you see the common factors in each term?

we can't help you if you don't show any work.
 
is this a repeat post of the same problem?

This was previously posted in another thread!
 
Last edited:
Olly_price said:
Factorise:

2sinx cosx - 4sin^3x cosx
How's your algebra skills? If you can factorize this algebraic expression:
2xy - 4x3y
... then you should be able to factorize the original problem in a similar way.

Olly_price said:
I don't want just a simple explanation with an answer, I need a full explanation of every mathematical step.
Sorry, no can do. If this is homework, then giving solutions would be against the forum rules.
 
You simply MUST provide some intial steps on your own (you DO have that, right?)
THEN, we can help you along with some more!

While your expression can most elegantly be expressed strictly in terms of a single sine function, with amplitude one half, you need to show some willingness to get there at least some part of the way.
 
Last edited:
Your steps are:

1. Call sin(x)=a, cos(x)=b and rewrite the expression.
2. Factor the expression with respect to a and b. (You know how to do that, right?)
3. Substitute the trigonometric functions back.
4. Write down the trigonometric identities you know.
5. If you still can't see the solution, please reply (show some working.)
 

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