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The image you provided contains a mathematical expression that appears to be written as follows:

\[
x^2 + xy + y^3 \quad \text{and} \quad x^3 - y^3
\]

It seems that after these expressions, the term "L.C.M." (Least Common Multiple) is written, followed by some additional notation.

It looks like the task is to find the Least Common Multiple (LCM) of the two algebraic expressions:

1. \(x^2 + xy + y^3\)
2. \(x^3 - y^3\)

Would you like a detailed explanation of how to find the LCM of these two expressions? Additionally, let me know if there's any part you'd like further clarification on!

Here are 5 related questions to deepen your understanding:
1. How do we calculate the LCM of two polynomials?
2. What are the factors of the polynomials \(x^2 + xy + y^3\) and \(x^3 - y^3\)?
3. How does factoring help in finding the LCM of two expressions?
4. Can you explain the difference between LCM and GCD (Greatest Common Divisor) for polynomials?
5. How can you simplify the expression \(x^3 - y^3\)?

**Tip:** When finding the LCM of algebraic expressions, factoring both expressions completely will help you find their common multiples more efficiently.

What is the Least Common Multiple (LCM) of the algebraic expressions x^2 + xy + y^3 and x^3 - y^3?

Explore how to find the Least Common Multiple (LCM) of two algebraic expressions: x^2 + xy + y^3 and x^3 - y^3. Learn key algebraic concepts and formulas, including factoring and polynomial expressions. Suitable for Grades 9-12.

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