Exploring Adding and Subtracting Rational Expressions

The video tutorial covers various methods of factoring polynomials, including the greatest common factor (GCF), difference of squares, sum of cubes, and difference of cubes. Each method is explained with examples, focusing on even-numbered problems. The tutorial provides step-by-step instructions for identifying and applying these factoring techniques, emphasizing the importance of recognizing perfect squares and cubes.

What is the Greatest Common Factor (GCF) of 14m^8n^5 and 7m^2n^2?

• 14m^2n^2

• 14m^8n^5

• 7m^8n^5

• 7m^2n^2

After factoring out the GCF from 16x^3y - 12x^2y^2 + 32xy^3, what is the remaining expression?

• 4x^2y^2 + 3xy^3 + 8y^4

• 4x^2 + 3xy + 8y^2

• 4x^2y + 3xy^2 + 8y^3

• 4x^3 + 3x^2y + 8xy^2

Which of the following is a perfect square?

• 30

• 25

• 15

• 50

What is the factored form of 9x^2 - 49y^2?

• (3x + 7y)(3x + 7y)

• (3x - 7y)(3x - 7y)

• (3x + 7y)(3x - 7y)

• (9x + 49y)(9x - 49y)

What is the rule for factoring a sum of cubes?

• a^3 + b^3 = (a + b)(a^2 - ab + b^2)

• a^3 + b^3 = (a - b)(a^2 + ab + b^2)

• a^3 + b^3 = (a + b)(a^2 + ab + b^2)

• a^3 + b^3 = (a - b)(a^2 - ab + b^2)

What is the factored form of 8w^3 + 1?

• (2w - 1)(4w^2 + 2w + 1)

• (2w + 1)(4w^2 - 2w + 1)

• (2w + 1)(4w^2 + 2w + 1)

• (2w - 1)(4w^2 - 2w + 1)

What is the rule for factoring a difference of cubes?

• a^3 - b^3 = (a + b)(a^2 - ab + b^2)

• a^3 - b^3 = (a + b)(a^2 + ab + b^2)

• a^3 - b^3 = (a - b)(a^2 + ab + b^2)

• a^3 - b^3 = (a - b)(a^2 - ab + b^2)

What is the factored form of 64 - w^3?

• (4 + w)(16 - 4w + w^2)

• (4 - w)(16 + 4w + w^2)

• (4 + w)(16 + 4w + w^2)

• (4 - w)(16 - 4w + w^2)

What is the factored form of x^3 - 27y^3?

• (x + 3y)(x^2 + 3xy + 9y^2)

• (x - 3y)(x^2 + 3xy + 9y^2)

• (x + 3y)(x^2 - 3xy + 9y^2)

• (x - 3y)(x^2 - 3xy + 9y^2)

What is the GCF of 24 and 375?

• 5

• 6

• 3

• 2