Factoring Expressions and Cubes

The video tutorial explains how to factor the expression 40c^3 - 5d^3. It begins by identifying the common factor of 5 and factoring it out. The tutorial then recognizes 8c^3 as a perfect cube and introduces the difference of cubes formula. The instructor demonstrates how to apply this formula to factor the expression completely, resulting in the final factored form: 5(2c - d)(4c^2 + 2cd + d^2).

What is the first step in factoring the expression 40c^3 - 5d^3?

• Expand the expression

• Identify the greatest common factor

• Apply the quadratic formula

• Use the sum of cubes formula

What is the result of factoring out the common factor from 40c^3 - 5d^3?

• 5(8c^3 + d^3)

• 8(5c^3 - d^3)

• 8(5c^3 + d^3)

• 5(8c^3 - d^3)

What is the perfect cube form of the number 8 in the expression?

• 3^2

• 2^3

• 4^2

• 5^3

Which formula is used to factor a difference of cubes?

• a^2 + b^2 = (a + 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^2 - b^2 = (a - b)(a + b)

In the expression a^3 - b^3, what does 'a' represent in the context of 2c?

• 2c

• d

• 2

• c

What is the expression for a squared in the context of 2c?

• 8c^3

• 4c^2

• 2c

• c^2

What is the purpose of pattern matching in this context?

• To simplify the expression

• To apply the difference of cubes formula

• To identify the greatest common factor

• To expand the expression

What is the final factored form of the expression 40c^3 - 5d^3?

• 5(2c - d)(4c^2 + 2cd + d^2)

• 5(2c + d)(4c^2 + 2cd + d^2)

• 5(2c + d)(4c^2 - 2cd + d^2)

• 5(2c - d)(4c^2 - 2cd + d^2)

What is the term for the expression 2c times d?

• 4cd

• c^2d

• cd

• 2cd

What is the final step in simplifying the factored expression?

• Remove one set of parentheses

• Add a set of parentheses

• Multiply the terms

• Divide the terms