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

2 min read Jun 17, 2024

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

This expression looks complex at first glance, but we can simplify it using some algebraic manipulations. Let's break it down step by step:

First, notice that the numerator consists of two squared terms: (x+5)^2 and (x-5)^2. This pattern fits the difference of squares formula:

a² - b² = (a + b)(a - b)

Let's apply this to our numerator:

(x+5)^2(x-5)^2 = [(x+5)(x-5)]^2

Now, we can expand the square in the numerator:

[(x+5)(x-5)]^2 = (x² - 25)²

Finally, we can substitute this simplified numerator back into the original expression:

(x² - 25)² / (x² + 25)

This expression is now in its simplest form. We can't simplify it further without knowing the specific value of x.

Recognizing patterns like the difference of squares is crucial for simplification.
Expanding and simplifying expressions can lead to more manageable forms.
Sometimes, an expression can't be simplified further without specific values for variables.