How do I simplify this calculus problem?

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In summary, the conversation is about a calculus problem where the equation 2x + 3 (y-x)^2 * (y'-1) = 0 is given and the answer requires the equation 2x + 3 (y-x)^2 * y'- 3 (y-x)^2 = 0. The solution involves using the given values of a, b, and c to rewrite the equation as 3a(b-c) = 3ab - 3ac.
  • #1
tmt1
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Hi I'm working on a problem for calculus

and I got this

2x + 3 (y-x)^2 * (y'-1) = 0 .

And then, in the answer part it says I have to get to here, which I'm not sure how to do.

2x + 3 (y-x)^2 * y'- 3 (y-x)^2 = 0 ,

Thanks,

Tim
 
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  • #2
tmt said:
Hi I'm working on a problem for calculus

and I got this

2x + 3 (y-x)^2 * (y'-1) = 0 .

And then, in the answer part it says I have to get to here, which I'm not sure how to do.

2x + 3 (y-x)^2 * y'- 3 (y-x)^2 = 0 ,

Thanks,

Tim

It's [tex]\displaystyle \begin{align*} 3a\left( b - c \right) = 3a\,b - 3a\,c \end{align*}[/tex], where [tex]\displaystyle \begin{align*} a = \left( y - x \right) ^2 , b = y', c = 1 \end{align*}[/tex].
 

FAQ: How do I simplify this calculus problem?

1. What are simplification problems?

Simplification problems are mathematical or logical problems that involve simplifying an expression or equation to its most basic form. This is often done by combining like terms, using the distributive property, or applying other simplification rules.

2. Why are simplification problems important?

Simplification problems are important because they help us understand and manipulate complex mathematical expressions and equations. They also help us solve more complicated problems by breaking them down into smaller, more manageable parts.

3. How do I solve a simplification problem?

The first step in solving a simplification problem is to carefully read and understand the given expression or equation. Then, you can use known simplification rules and techniques to simplify the expression or equation. Finally, check your answer to ensure it is in its simplest form.

4. What are some common mistakes to avoid when solving simplification problems?

One common mistake is forgetting to apply the correct simplification rules or making arithmetic errors. It is also important to be careful with negative signs and exponents, as they can easily be overlooked or misinterpreted.

5. How can I improve my skills in solving simplification problems?

The best way to improve your skills in solving simplification problems is to practice regularly. You can also seek help from a teacher or tutor, study examples, and familiarize yourself with common simplification rules and techniques. Additionally, breaking down more complex problems into simpler ones can also help improve your skills.

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