Multiply. (2 x^2-5 x)/(2 x y+y) ·(2 x y^2+y^2)/(5 x^2-2 x^3)...

Name: Problem 45, Chapter 11: Prealgebra and Introductory Algebra
Uploaded: 2020-06-24T20:07:11-08:00
Duration: 2 min 50 s
Channel: Susan Cooper
Description: Multiply. (2 x^2-5 x)/(2 x y+y) ·(2 x y^2+y^2)/(5 x^2-2 x^3)

Key Concepts

Multiplying Rational Expressions

This involves multiplying two fractions that contain polynomials in the numerator and denominator. The process includes multiplying the numerators together and the denominators together to create a single rational expression. It is a fundamental skill in algebra that underlies more advanced operations with rational expressions.

Polynomial Factorization

Factoring is the process of breaking down a polynomial into products of simpler polynomials that, when multiplied together, give the original polynomial. It is an essential technique for simplifying expressions and solving equations, as it often reveals common factors that can be canceled from the numerator and the denominator.

Simplification of Expressions

After multiplying the rational expressions and factoring the resulting polynomials, simplification involves canceling any common factors that appear in both the numerator and the denominator. This step is crucial for reducing the expression to its simplest form and is widely used in algebra to handle complex equations efficiently.

Domain Restrictions

When working with rational expressions, it is important to identify the values of the variables that would make any denominator zero, as these values are excluded from the domain of the expression. Recognizing domain restrictions ensures that the solution set is correctly identified and that the expression is properly defined.

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