Factoring Expressions and Difference of Squares

The video tutorial explains how to simplify and factor a quadratic expression using the difference of squares method. It begins by factoring out a common factor, then applies the difference of squares rule to simplify the expression further. The tutorial provides a step-by-step approach to reach the final factored solution, emphasizing the importance of recognizing squared terms and their differences.

What is the first step in simplifying the expression 45x² - 125?

• Factor out a 5 from both terms

• Add 5 to both terms

• Divide both terms by 9

• Multiply both terms by 5

After factoring out a 5, what does the expression 45x² - 125 become?

• 9x² - 25

• 5x² - 25

• 45x² - 25

• 9x² - 125

What is the difference of squares rule used for?

• Subtracting two squared terms

• Multiplying two squared terms

• Adding two squared terms

• Dividing two squared terms

How can 9x² be expressed as a square?

• (3x)²

• (x)²

• (9x)²

• (3)²

What is the square of 5 in the expression 9x² - 25?

• 10

• 5

• 25

• 15

What is the final factored form of the expression 45x² - 125?

• 5(3x + 5)(x - 5)

• 5(3x + 25)(3x - 25)

• 5(9x + 5)(9x - 5)

• 5(3x + 5)(3x - 5)

Why is it important to remember the difference of squares rule?

• It simplifies addition problems

• It helps in solving subtraction problems involving squares

• It is used for division of squares

• It is used for multiplication of squares

What is the benefit of using the difference of squares in factoring?

• It simplifies the expression

• It makes the expression more complex

• It changes the expression to addition

• It eliminates the need for factoring

What should you not forget when writing the final answer after using the difference of squares?

• The original expression

• The common factor factored out initially

• The addition sign

• The subtraction sign