Pythagorean Theorem and Factoring Concepts

This video tutorial covers the concept of factoring differences of squares, using algebra tiles, and various methods and patterns for factoring binomials. It includes examples of factoring complex polynomials and demonstrates mental math techniques using differences of squares. The lesson also explores the Pythagorean theorem and how to find Pythagorean triples.

What is the first step in factoring x^2 - 9 using algebra tiles?

• Arrange the tiles into a rectangle

• Model x^2 - 9 with tiles

• Use the FOIL method

• Find the length and width

Which of the following is the correct factorization of M^2 - 81 using the difference of squares pattern?

• (M - 1)(M + 1)

• (M - 81)(M + 81)

• (M - 8)(M + 8)

• (M - 9)(M + 9)

What is the greatest common factor (GCF) of 100s^2 - 25t^2?

• 10

• 25

• 5

• 50

When factoring a binomial with common factors, what should be done first?

• Apply the difference of squares

• Use the FOIL method

• Complete the square

• Factor out the GCF

In the example 3K^4 - 48, what is the GCF that is factored out first?

• 3

• 12

• 16

• 4

How can the difference of squares be used to multiply 37 and 43 mentally?

• By squaring 40 and subtracting the square of 3

• By multiplying 37 by 43 directly

• By using the FOIL method

• By adding 37 and 43

According to the Pythagorean theorem, what is the relationship between the sides of a right triangle?

• a^2 = b^2 + c^2

• a^2 + b^2 = c^2

• a^2 + b^2 = c

• a + b = c^2

What is a Pythagorean triple?

• A set of three numbers that form a right triangle

• A set of three numbers that satisfy a^2 + b^2 = c^2

• A set of three numbers that are all even

• A set of three numbers that are all odd

In the example of finding a Pythagorean triple with 8, what are the two factors of 64?

• 4 and 16

• 8 and 8

• 2 and 32

• 1 and 64

What is the Pythagorean triple that includes 8?

• 8, 12, 16

• 8, 14, 18

• 8, 15, 17

• 8, 10, 18