Multiply and simplify. See Example 6 (2 x^2+12 x-32)/(x^2+16 x+64) ·(x^2+10 x+16)/(x^2-3 x-10)

Name: Problem 44, Chapter 6: Intermediate Algebra
Uploaded: 2020-07-16T19:21:38-08:00
Duration: 1 min 38 s
Channel: Amy Jiang
Description: Multiply and simplify. See Example 6 (2 x^2+12 x-32)/(x^2+16 x+64) ·(x^2+10 x+16)/(x^2-3 x-10)

step 1 Okay, so we want to simplify defaulting. So let's note for this time, we can factor a 2, and the

Multiply and simplify. See Example 6 (2 x^2+12 x-32)/(x^2+16...

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Key Concepts

Polynomial Factoring

This involves rewriting a polynomial as a product of simpler polynomials or binomials, which can reveal common factors and simplify the expression. It includes techniques such as factoring quadratic expressions, grouping, and using special factorization formulas like the difference of squares.

Multiplication of Rational Expressions

This refers to the process of multiplying two or more fractions where both the numerator and denominator are polynomials. The key step is to multiply the numerators together and the denominators together, giving a new rational expression that can often be simplified further.

Simplification through Canceling Common Factors

After multiplying rational expressions, some factors in the numerator and denominator might be identical. Canceling these common factors is essential for reducing the expression to its simplest form. This step is possible only when the factors are non-zero, ensuring that the domain restrictions of the original expression are respected.

Domain Considerations

When simplifying rational expressions, it is important to take into account values of the variable that make any denominator zero. These values, which are excluded from the domain, must be noted both before and after simplification to avoid erroneous conclusions about the equivalence of expressions.

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