Since $$x^3 - y^3 = (x - y)(x^2 + xy + y^2)$$ then $$x^5 - y^5 = (x^{5/3})^3 - (y^{5/3})^3= (x^{5/3} - y^{5/3})((x^{5/3})^2 + x^{5/3}y^{5/3}+(y^{5/3})^2)$$
It looks very wrong to me, but I can't find the algebra mistake
2026-04-16 11:07:45.1776337665
Why is this reasoning of factor wrong?
82 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ALGEBRA-PRECALCULUS
- How to show that $k < m_1+2$?
- What are the functions satisfying $f\left(2\sum_{i=0}^{\infty}\frac{a_i}{3^i}\right)=\sum_{i=0}^{\infty}\frac{a_i}{2^i}$
- Finding the value of cot 142.5°
- Why is the following $\frac{3^n}{3^{n+1}}$ equal to $\frac{1}{3}$?
- Extracting the S from formula
- Using trigonometric identities to simply the following expression $\tan\frac{\pi}{5} + 2\tan\frac{2\pi}{5}+ 4\cot\frac{4\pi}{5}=\cot\frac{\pi}{5}$
- Solving an equation involving binomial coefficients
- Is division inherently the last operation when using fraction notation or is the order of operation always PEMDAS?
- How is $\frac{\left(2\left(n+1\right)\right)!}{\left(n+1\right)!}\cdot \frac{n!}{\left(2n\right)!}$ simplified like that?
- How to solve algebraic equation
Related Questions in SOLUTION-VERIFICATION
- Linear transform of jointly distributed exponential random variables, how to identify domain?
- Exercise 7.19 from Papa Rudin: Gathering solutions
- Proof verification: $\forall n \in \mathbb{Z}, 4\nmid(n^2+2)$
- Proof verification: a function with finitely many points of discontinuity is Riemann integrable
- Do Monoid Homomorphisms preserve the identity?
- Cantor-Lebesgue's theorem
- If $a$ is an integer, prove that $\gcd(14a + 3, 21a + 4) = 1$.
- Number theory gcd
- $|G| > 1$ and not prime implies existence of a subgroup other than two trivial subgroups
- Prove/Disprove: Sum of im/ker of linear transformation contained in ker/im of each linear trasnfromation
Related Questions in FACTORING
- Roots of a complex equation
- Solving for 4 variables using only 2 equations
- For any natural numbers a, b, c, d if a*b = c*d is it possible that a + b + c + d is prime number
- How can I calculate the remainder of $3^{2012}$ modulo 17?
- The complex equation $x^3 = 9 + 46i$ has a solution of the form $a + bi$ where $a,b\in \mathbb Z$. Find the value of $a^3 + b^3$
- Conversion factor
- How do I find roots of the 3rd order polynomial?
- How to find algorithm for integer factorization if the prime factorization of the integer is given?
- Define a binary operation * on the real numbers as $x * y=xy+x+y$ for all real numbers x and y.
- Computing $\lim_{x \to 1}\frac{x^\frac{1}{5}-1}{x^\frac{1}{6} -1}$
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
It's not wrong, and it's a nice thought! But...
Although this is not wrong, it's not a particularly nice factorization because the exponents are not natural numbers. You could just as correctly say that $x^3-y^3=(x^{3/2}-y^{3/2})(x^{3/2}+y^{3/2})$, but this similarly would not be very nice.
Now, it happens that $x^5-y^5$ does have a nice factorization in this way, which is why we can be picky on this point. Perhaps if there was no such factorization to be had, we could accept a solution with rational exponents.