step 1 We want to divide y -qued plus 27, but I would say plus 0 y squared plus 0 -Y plus 27 by y plus

(y^3+27)/(y+3) | Numerade

Name: Problem 69, Chapter 4: Beginning and Intermediate Algebra
Uploaded: 2022-02-11T00:26:46-08:00
Duration: 55 s
Channel: James Kiss
Description: (y^3+27)/(y+3)

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Key Concepts

Sum of Cubes Identity

This concept refers to the algebraic identity a³ + b³ = (a + b)(a² - ab + b²), which allows us to factor expressions that represent the sum of two cubes. Understanding this identity is essential for recognizing and simplifying expressions of the form y³ + 27 by noticing that 27 is a cube (3³).

Polynomial Factorization

Polynomial factorization involves expressing a polynomial as a product of its factors. In the context of the given expression, factoring y³ + 27 using the sum of cubes identity simplifies the rational expression by breaking it down into factors that can potentially cancel with terms in the denominator.

Simplification of Rational Expressions

This concept deals with reducing a rational expression to its simplest form by canceling out common factors in the numerator and the denominator. By factoring the numerator using the sum of cubes identity, one can cancel the common factor in the denominator, provided that the cancellation is valid within the domain of the expression (i.e., the denominator is not zero).

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