Factoring and Simplifying Expressions

The video tutorial explains how to subtract rational expressions by finding the least common multiple (LCM) of the denominators. It begins with an introduction to the problem, followed by factoring the expressions to identify the LCM. The tutorial demonstrates factoring using the difference of squares and grouping methods. Once the common denominator is determined, the expressions are rewritten with this denominator, and the numerators are adjusted accordingly. Finally, the expression is simplified to reach the solution.

What is the first step in subtracting rational expressions?

• Add the numerators directly.

• Find the least common multiple of the denominators.

• Divide the expressions.

• Multiply the expressions.

How is the expression 9x^2 - 49 factored?

• (3x + 7)(3x + 7)

• (3x - 7)(3x - 7)

• (3x + 7)(3x - 7)

• (3x - 7)(x + 4)

Which method is used to factor the expression 3x^2 + 5x - 28?

• Difference of squares

• Completing the square

• Quadratic formula

• Grouping

What is the common factor in the expression 3x^2 + 5x - 28 after grouping?

• x + 4

• 3x - 7

• 3x + 7

• x - 4

What must be included in the least common multiple of the denominators?

• None of the above

• All factors from both expressions

• Only the factors of the second expression

• Only the factors of the first expression

What additional factor is needed in the LCM that is not in the first expression?

• 3x + 7

• 3x - 7

• x + 4

• x - 4

What do you multiply the numerator of the first expression by to match the LCM?

• 3x + 7

• 3x - 7

• x + 4

• x - 4

What is the result of multiplying 4 by (x + 4)?

• 4x + 16

• 4x + 4

• 4x - 4

• 4x - 16

What is the simplified form of the numerator after subtraction?

• x - 7

• x + 7

• x - 9

• x + 9

What is the final denominator of the simplified expression?

• (3x + 7)(3x - 7)

• (3x + 7)(3x - 7)(x + 4)

• (3x - 7)(x + 4)

• (3x + 7)(x + 4)