Factoring the Difference of Two Squares

This video tutorial introduces the concept of factoring using the difference of two squares formula. It explains what perfect squares are and how they are used in this method. The tutorial provides step-by-step instructions on applying the formula, along with examples and practice problems. Advanced techniques and considerations are discussed, including working backwards from factored forms. The video concludes with a summary of the key points and encourages further practice.

What is required knowledge before learning the difference of two squares?

• Factoring trinomials

• Solving quadratic equations

• Graphing linear equations

• Understanding exponential functions

What defines a perfect square in mathematics?

• A number that can be expressed as the product of two equal integers

• A number that can be divided by two without a remainder

• A number that is the sum of two equal integers

• A number that is the result of adding two prime numbers

How does the difference of two squares formula factorize a squared minus b squared?

• (a - b)(a + b)

• (a + b)(a - b)

• (a + b)^2

• (a - b)^2

What is the factored form of x^2 - 49 using the difference of two squares?

• (x - 49)(x + 49)

• (x - 7)(x + 7)

• (x + 7)(x - 7)

• x^2 - 7^2

When can the difference of two squares formula not be used directly?

• All of the above

• When the expression involves subtraction of non-square terms

• When the expression is a sum of squares

• When the expression is a product of squares

What additional step might be needed before applying the difference of two squares formula?

• Multiplying each term by two

• Converting all terms to square roots

• Factoring out the greatest common factor

• None of the above

How can coefficients affect the application of the difference of two squares formula?

• Any coefficient can be used without restrictions

• Coefficients must be prime numbers

• Coefficients do not affect the formula

• Coefficients must be perfect squares themselves

What is the factored form of 36x^2 - 121 using the difference of two squares?

• (6x + 11)(6x - 11)

• 36x^2 - 11^2

• (6x - 11)(6x + 11)

• (36x - 121)(36x + 121)

How can the difference of two squares formula be used to simplify factoring when adding squares?

• It cannot be used for addition of squares

• By converting addition into subtraction

• By applying the formula directly

• By multiplying each term by -1

What is the correct backward application of the difference of two squares for the expression (3t - 9)(3t + 9)?

• 3t^2 - 81

• 9t^2 - 81

• t^2 - 81

• 3t^2 - 9