Factor expression A so that it looks like expression B

  • Thread starter Thread starter sharpycasio
  • Start date Start date
  • Tags Tags
    Expression
AI Thread Summary
The discussion focuses on factoring the expression -a^2b + ab^2 + a^2c - b^2c - ac^2 + bc^2 into the form -(a-b)(a-c)(b-c). The user initially struggles with the factorization process but makes progress by rearranging the terms. They express the equation in a different format, leading to a clearer path for factoring. The conversation highlights the importance of rearranging terms to facilitate the factoring process. Ultimately, the user expresses gratitude for the assistance received in solving the problem.
sharpycasio
Messages
16
Reaction score
0

Homework Statement


This question stems from this one: https://www.physicsforums.com/showthread.php?t=642712

I think I know how to solve it now. The only problem is I have to show how to factor this expression into the form WolframAlpha shows.

-a^2 b + a b^2 + a^2 c - b^2 c - a c^2 + b c^2 → -(a-b)(a-c)(b-c)

Homework Equations


The Attempt at a Solution



I did this but then I don't know how to proceed.

ab(b-a)+ac(a-c)+bc(c-b)

Please help. Thanks
 
Physics news on Phys.org
By rearranging it like so:
−a^2b+ab^2+a^2c−b^2c−ac^2+bc^2 \rightarrow −a^2b+a^2c+ab^2−ac^2−b^2c+bc^2
 
Last edited:
You're a genius! Thank you. :)
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
View full post »

Similar threads

Arithmetic mean and geometric mean
Replies
1
Views
2K
Equality of sums of powers
Replies
47
Views
5K
Use Remainder theorem to find factors of ##(a-b)^3+(b-c)^3+(c-a)^3##
Replies
4
Views
2K
The value of (b - c) / (c - a)
Replies
11
Views
3K
Proving one equation, cyclic in variables ##a,b,c##, to another
Replies
4
Views
2K
Solving these Simultaneous Equations
Replies
3
Views
2K
Prove that terms cyclic in ##a,b,c##, are in ##\text{AP}##
Replies
7
Views
2K
Show that ##(b-c)x^2+(c-a)x+a-b=0## has rational roots
Replies
11
Views
2K
Can Logarithms Be Used to Solve a Tricky Exponential Problem?
Replies
5
Views
2K
Trig problem involving a triangle's angles and sides
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top