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(x^3+y^3)/(x-y)

2 min read Jun 17, 2024
(x^3+y^3)/(x-y)

Factoring the Expression (x³ + y³) / (x - y)

The expression (x³ + y³) / (x - y) can be simplified by factoring the numerator. Here's how:

Understanding the Sum of Cubes Pattern

The numerator, x³ + y³, follows the pattern of the sum of cubes:

a³ + b³ = (a + b)(a² - ab + b²)

Applying the Pattern

  1. Identify 'a' and 'b': In our expression, a = x and b = y.
  2. Substitute into the pattern: (x³ + y³) = (x + y)(x² - xy + y²)

Simplifying the Expression

Now we have:

(x³ + y³) / (x - y) = [(x + y)(x² - xy + y²)] / (x - y)

The expression cannot be further simplified. However, it is now factored, making it easier to work with in other equations or calculations.

Note:

  • The expression (x² - xy + y²) in the factored form cannot be factored further using real numbers.
  • The expression is undefined when x = y. This is because the denominator (x - y) would become zero, leading to an undefined result.

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