x³ + y³ using sum and difference of two cubes

To factor the expression \(x^3 + y^3\) using the sum of two cubes, you can apply the following formula:

\[
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
\]

For your expression \(x^3 + y^3\), substitute \(a = x\) and \(b = y\) into the formula:

\[
x^3 + y^3 = (x + y)(x^2 - xy + y^2)
\]

So, the factorization of \(x^3 + y^3\) is:

\[
x^3 + y^3 = (x + y)(x^2 - xy + y^2)
\]

### Do you have any questions, or would you like further details?

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**Related Questions:**

1. How do you factor the difference of two cubes, \(x^3 - y^3\)?
2. Can you explain why the formula for the sum of cubes works?
3. What is the geometric interpretation of the sum of cubes?
4. How can the sum of cubes be applied in solving algebraic equations?
5. What is the relationship between the sum of cubes and the binomial theorem?
6.

Learn how to factorize x^3 + y^3 using the sum of cubes formula. This problem explores key algebraic concepts, including cubic equations and the sum of cubes formula. Suitable for students in Grades 9-12.

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