(x-5)(x^2+5x+25)

Jasonbradley

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Jun 17, 2024

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Factoring the Expression: (x-5)(x^2 + 5x + 25)

This expression represents a special case of factoring known as the difference of cubes. Let's break down how it works:

Understanding the Difference of Cubes

The difference of cubes pattern states:

a³ - b³ = (a - b)(a² + ab + b²)

In our expression, we can identify:

• a = x
• b = 5

Applying the Pattern

1. Recognize the pattern: Notice that (x^2 + 5x + 25) is the result of squaring the first term (x), multiplying the first and second terms (x and 5), and squaring the second term (5). This confirms it matches the pattern.

2. Apply the formula: Substituting our values of 'a' and 'b' into the difference of cubes formula, we get:

   (x - 5)(x² + 5x + 25) = x³ - 5³

3. Simplify: This simplifies to:

   x³ - 125

Conclusion

Therefore, factoring (x-5)(x^2 + 5x + 25) using the difference of cubes pattern results in x³ - 125.