Factoring Cubes and Powers

The video tutorial by Amal Kumar covers the process of factoring expressions with higher powers, specifically focusing on the difference of cubes. The example used is 27x^9 - 125y^18, which is broken down into its cube components. The tutorial explains how to apply the difference of cubes formula, resulting in a factored expression that cannot be further simplified. The video concludes with a summary of the steps and the formula used.

What is the first step in factoring higher powers?

• Identify the expression as a difference of squares

• Identify the expression as a sum of squares

• Identify the expression as a difference of cubes

• Identify the expression as a sum of cubes

How can 27 be expressed as a cube?

• 4^3

• 2^3

• 5^3

• 3^3

What is the cube root of x^9?

• x^5

• x^4

• x^3

• x^2

How can 125 be expressed as a cube?

• 6^3

• 4^3

• 3^3

• 5^3

What is the cube root of y^18?

• y^6

• y^5

• y^4

• y^3

What is the formula for the 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 first term in the factorization of 27x^9 - 125y^18?

• 3x^3 + 5y^6

• 3x^3 - 5y^6

• 5x^3 + 3y^6

• 5x^3 - 3y^6

What is the square of the first term in the factorization?

• 9x^9

• 9x^12

• 9x^3

• 9x^6

What is the product of the first and second terms in the factorization?

• 15x^3y^6

• 15x^6y^9

• 15x^9y^6

• 15x^6y^3

What is the square of the second term in the factorization?

• 25y^18

• 25y^12

• 25y^6

• 25y^24