Difference of Squares and Factoring

The video tutorial explains how to solve the equation x^2 - 44 = 100 using two methods: recognizing the difference of two perfect squares and solving it algebraically. The instructor demonstrates the steps to transform the equation into x^2 - 144 = 0, which can be rewritten as (x - 12)(x + 12) = 0. This leads to the solutions x = 12 and x = -12, corresponding to answer choice C.

What is the initial equation presented in the problem?

• x^2 + 44 = 100

• x^2 - 44 = 100

• x^2 - 100 = 44

• x^2 + 100 = 44

Which of the following is a method to solve the equation x^2 - 44 = 100?

• Using the quadratic formula

• Recognizing the difference of two perfect squares

• Completing the square

• Graphing the equation

What is the formula for the difference of two perfect squares?

• a^2 + b^2 = (a + b)(a - b)

• a^2 + b^2 = (a - b)^2

• a^2 - b^2 = (a - b)(a + b)

• a^2 - b^2 = (a + b)^2

How is the equation x^2 - 44 = 100 rewritten using the difference of squares?

• x^2 - 144 = 0

• x^2 + 12^2 = 0

• x^2 - 12^2 = 0

• x^2 - 100 = 44

What is the value of b in the expression x^2 - b^2 = 0?

• 13

• 12

• 11

• 10

What are the factors of the equation x^2 - 12^2 = 0?

• (x - 13)(x + 13)

• (x - 11)(x + 11)

• (x - 10)(x + 10)

• (x - 12)(x + 12)

What are the solutions to the equation (x - 12)(x + 12) = 0?

• x = 12 or x = -12

• x = 10 or x = -10

• x = 11 or x = -11

• x = 13 or x = -13