Rational Functions: Expansion Techniques

The video tutorial explains how to convert rational functions from factored form to expanded form using distribution and the FOIL method. It covers three examples, demonstrating the step-by-step process of expanding factors and combining like terms to achieve the expanded form. The tutorial emphasizes the use of distribution and provides a visual approach to simplify the conversion process.

What is the first step in converting a rational function from factored to expanded form?

• Identify the common factors.

• Simplify the expression.

• Add all terms together.

• Use the distributive property or FOIL method.

In Example 5, what is the expanded form of the expression with the denominator x(x + 4)?

• x^2 + 4x

• x^2 + 8x

• x^2 + 2x

• x^2 + 4

What is the purpose of using the distributive property in Example 5?

• To find the greatest common factor.

• To simplify the expression.

• To expand the expression into a polynomial.

• To factor the expression further.

In Example 5, what is the expanded form of the numerator?

• x + 2

• x^2 + 4x

• x^2 + 4

• x + 4

In Example 5, what is the expanded form of the expression with the numerator x + 4?

• x + 2

• x + 4

• x^2 + 4

• x^2 + 4x

What is the result of combining like terms in Example 5's denominator?

• x^2 + 3x

• x^2 + 2x

• x^2 + 4x

• x^2 + x

In Example 6, what is the result of multiplying x by (x - 3)?

• x^2 + 6

• x^2 - 3x

• x^2 + 3x

• x^2 - 6

What is the expanded form of the denominator in Example 6?

• x^2 + 2x - 3

• x^2 + 3x - 1

• x^2 - 2x - 3

• x^2 - 3x + 1

What is the next step after using distribution in Example 6?

• Combine like terms.

• Simplify the expression.

• Add all terms together.

• Factor the expression.

In Example 6, what is the expanded form of the numerator?

• x + 1

• x^2 + 1

• x^2 + x

• x + 2