Multiply and simplify. See Example 6 (2 x^2-2)/(10 x+30) ·(12 x+36)/(3 x-3)

Name: Problem 38, Chapter 6: Intermediate Algebra
Uploaded: 2020-07-16T19:07:54-08:00
Duration: 59 s
Channel: Amy Jiang
Description: Multiply and simplify. See Example 6 (2 x^2-2)/(10 x+30) ·(12 x+36)/(3 x-3)

step 1 Okay, so we want to simplify the following. Well, let's note for this term, we can factor out of

Multiply and simplify. See Example 6 (2 x^2-2)/(10 x+30)...

Key Concepts

Common Factor Extraction

Common factor extraction involves identifying and factoring out terms that are common across all parts of a polynomial. This simplification step not only makes the polynomial easier to factor further but also allows for the cancellation of these common factors in rational expressions, essential for efficient simplification.

Multiplication of Rational Expressions

This concept involves multiplying the numerators together and the denominators together to combine two or more rational expressions into a single fraction. It sets the stage for simplifying the expression further by allowing one to express the combined product as one fraction that can then be factored and reduced by eliminating common factors from the numerator and denominator.

Factorization Techniques

Factorization is the process of rewriting a polynomial as the product of its factors. This includes recognizing common factors, factorizations such as differences of squares, and extracting similar terms. Factoring polynomials is essential to simplify rational expressions since it exposes common factors that can be canceled.

Cancellation of Common Factors

After factoring the polynomials in the numerator and denominator, any factors that appear in both can be canceled, provided they are not zero. This step dramatically simplifies the expression and is key to arriving at the simplest form of the rational expression.

Transcript

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