Simplify the following expression by factoring.  Identify the factors below that would leave your answer in the simplest factored form. 121x6 - 100y6

1. Break Down the Problem

We need to simplify the expression $121x^6 - 100y^6$ by factoring. This expression is a difference of squares since it can be represented as $a^2 - b^2$.

2. Relevant Concepts

Recall the difference of squares formula: $a^2 - b^2 = (a - b)(a + b)$ Identify $a^2$ and $b^2$ in the given expression:

• $a^2 = 121x^6$ implies $a = 11x^3$
• $b^2 = 100y^6$ implies $b = 10y^3$

3. Analysis and Detail

Using the difference of squares formula: $121x^6 - 100y^6 = (11x^3 - 10y^3)(11x^3 + 10y^3)$ Now we can check if each factor can be further factored.

4. Verify and Summarize

The factors $11x^3 - 10y^3$ and $11x^3 + 10y^3$ do not factor over the integers since they are not further reducible using real numbers. Therefore, our expression is in its simplest factored form.

Final Answer

The simplified expression by factoring is: $(11x^3 - 10y^3)(11x^3 + 10y^3)$