In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition. Expansion of a polynomial expression can be obtained by repeatedly replacing subexpressions that multiply two other subexpressions, at least one of which is an addition, by the equivalent sum of products, continuing until the expression becomes a sum of (repeated) products. During the expansion, simplifications such as grouping of like terms or cancellations of terms may also be applied. Instead of multiplications, the expansion steps could also involve replacing powers of a sum of terms by the equivalent expression obtained from the binomial formula; this is a shortened form of what would happen if the power were treated as a repeated multiplication, and expanded repeatedly. It is customary to reintroduce powers in the final result when terms involve products of identical symbols. Simple examples of polynomial expansions are the well known rules when used from left to right. A more general single-step expansion will introduce all products of a term of one of the sums being multiplied with a term of the other: An expansion which involves multiple nested rewrite steps is that of working out a Horner scheme to the (expanded) polynomial it defines, for instance . The opposite process of trying to write an expanded polynomial as a product is called polynomial factorization. (Wikipedia).
Factor a polynomial expression completely over real numbers
Learn how to factor higher order trinomials. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. To factor an algebraic expression means to break it up into expressions that can be multiplied togeth
From playlist How to Factor Higher Order #Polynomial
What is the remainder theorem for polynomials
👉 Learn about the remainder theorem and the factor theorem. The remainder theorem states that when a polynomial is divided by a linear expression of the form (x - k), the remainder from the division is equivalent to f(k). Similarly, when a polynomial is divided by a linear expression of th
From playlist Remainder and Factor Theorem | Learn About
Factoring a polynomial raised to the 4th power
Learn how to factor higher order trinomials. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. To factor an algebraic expression means to break it up into expressions that can be multiplied togeth
From playlist How to Factor Higher Order #Polynomial
Factoring a binomial using the difference of two cubes
👉 Learn how to factor polynomials using the sum or difference of two cubes. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. To factor an algebraic expression means to break it up into expression
From playlist How to factor a polynomial to a higher power
Factoring by using a sum of cubes - Online tutor
👉 Learn how to factor polynomials using the sum or difference of two cubes. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. To factor an algebraic expression means to break it up into expression
From playlist How to factor a polynomial to a higher power
Factoring when your a and c are squared
Learn how to factor higher order trinomials. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. To factor an algebraic expression means to break it up into expressions that can be multiplied togeth
From playlist How to Factor Higher Order #Polynomial
Factoring a binomial to the fourth power by the difference of two squares
👉 Learn how to factor polynomials using the difference of two squares for polynomials raised to higher powers. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. To factor an algebraic expression m
From playlist How to factor a polynomial by difference of two squares
10c Machine Learning: Polynomial Regression
Lecture on polynomial regression, including an intuitive alternative interpretation, basis expansion concepts and orthogonal basis through Hermite polynomials. Follow along with the demonstration workflow: https://github.com/GeostatsGuy/PythonNumericalDemos/blob/master/SubsurfaceDataAnaly
From playlist Machine Learning
Xavier Ros-Oton: Regularity of free boundaries in obstacle problems, Lecture IV
Free boundary problems are those described by PDE that exhibit a priori unknown (free) interfaces or boundaries. Such type of problems appear in Physics, Geometry, Probability, Biology, or Finance, and the study of solutions and free boundaries uses methods from PDE, Calculus of Variations
From playlist Hausdorff School: Trending Tools
Analytic Shape Reconstruction of a Planar Conductivity Inclusion
43rd Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series Talk Date: Wednesday, April 27, 10:00am Eastern Speaker: Mikyoung Lim, KAIST Abstract: A conductivity inclusion inserted in a homogeneous background induces a perturbation in the background potential. The pe
From playlist Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series
How to integrate by partial fractions
Free ebook http://bookboon.com/en/learn-calculus-2-on-your-mobile-device-ebook How to integrate by the method of partial fraction decomposition. In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is a fraction such that the numerator
From playlist A second course in university calculus.
60 years of dynamics and number expansions - 11 December 2018
http://crm.sns.it/event/441/ 60 years of dynamics and number expansions Partially supported by Delft University of Technology, by Utrecht University and the University of Pisa It has been a little over sixty years since A. Renyi published his famous article on the dynamics of number expa
From playlist Centro di Ricerca Matematica Ennio De Giorgi
Manfred Madritsch: Normal and Non-Normal Numbers
CIRM HYBRID EVENT Recorded during the meeting "​ Diophantine Problems, Determinism and Randomness" the February 04, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathem
From playlist Probability and Statistics
Manfred Madritsch: The sum-of-digits function in linearly recurrent number systems and almost primes
CIRM VIRTUAL CONFERENCE Recorded during the meeting "​ Diophantine Problems, Determinism and Randomness" the November 27, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide
From playlist Virtual Conference
Conformal Bootstrap in Mellin Space by Aninda Sinha
11 January 2017 to 13 January 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru String theory has come a long way, from its origin in 1970's as a possible model of strong interactions, to the present day where it sheds light not only on the original problem of strong interactions, but
From playlist String Theory: Past and Present
Cynthia Vinzant: Log concave polynomials and matroids
Strong log concavity is a functional property of a real multivariate polynomial that translates to useful conditions on its coefficients and features in the polynomials defining several common conic programs. Recent work by several independent authors shows that the multivariate basisgener
From playlist Workshop: Tropical geometry and the geometry of linear programming
How to factor a polynomial using the difference of two cubes
👉 Learn how to factor polynomials using the sum or difference of two cubes. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. To factor an algebraic expression means to break it up into expression
From playlist How to factor a polynomial to a higher power
Martin Hairer Mini-course 1: Introduction to Regularity Structures
SMRI-MATRIX Symposium with Martin Hairer 17 February 2021: Mini-course 1 Title: Introduction to Regularity Structures Part 1 -----------------------------------------------------------------------------------------------------------------------------------------------------------------
From playlist Symposium with Martin Hairer
Francesco Mezzadri: Moments of Random Matrices and Hypergeometric Orthogonal Polynomials
We establish a new connection between moments of n×n random matrices $X_{n}$ and hypergeometric orthogonal polynomials. Specifically, we consider moments $\mathbb{E}\mathrm{Tr} X_n^{-s}$ as a function of the complex variable $s\in\mathbb{C}$, whose analytic structure we describe completely
From playlist Jean-Morlet Chair - Grava/Bufetov
👉 Learn about the remainder theorem and the factor theorem. The remainder theorem states that when a polynomial is divided by a linear expression of the form (x - k), the remainder from the division is equivalent to f(k). Similarly, when a polynomial is divided by a linear expression of th
From playlist Remainder and Factor Theorem | Learn About