(x%5E2%2B5x%2B25).jpeg "(x-5)(x^2+5x+25)")
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
-
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.
-
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
-
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.