Multiply and simplify. See Example 6 (18 a-12 a^2)/(4 a^2+4 a+1) ·(4 a^2+8 a+3)/(4 a^2-9)

Name: Problem 35, Chapter 6: Intermediate Algebra
Uploaded: 2020-07-16T18:54:18-08:00
Duration: 1 min 36 s
Channel: Amy Jiang
Description: Multiply and simplify. See Example 6 (18 a-12 a^2)/(4 a^2+4 a+1) ·(4 a^2+8 a+3)/(4 a^2-9)

step 1 Okay, so we want to factor out each term so we can simplify. Well, in our first term, this term

Multiply and simplify. See Example 6 (18 a-12 a^2)/(4 a^2+4...

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Key Concepts

Multiplication of Rational Expressions

In algebra, when multiplying rational expressions, you multiply the numerators together to create the new numerator and multiply the denominators together to form the new denominator. This process is analogous to the multiplication of fractions and often sets the stage for further simplification by revealing common factors between the new numerator and denominator.

Factoring Polynomials

Factoring polynomials is the process of expressing a polynomial as a product of simpler polynomials or monomials. This technique is crucial because it helps decompose complex expressions into factors that may cancel out when combined with similar expressions in a rational expression, thus simplifying the overall expression.

Canceling Common Factors

Canceling common factors involves identifying and removing identical factors present in both the numerator and denominator of a rational expression. This step is essential after factoring, as it significantly simplifies the expression and is reliant on the condition that the cancelled factor does not equal zero, preserving the equality of the expression.

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