Simplifying the Expression: (x^2 + 4x + 4)  (x^2  6x + 9)
This article aims to guide you through simplifying the given algebraic expression: (x^2 + 4x + 4)  (x^2  6x + 9).
Understanding the Expression
The expression involves two trinomials, each enclosed in parentheses:
 (x^2 + 4x + 4): This is a perfect square trinomial as it can be factored as (x + 2)^2.
 (x^2  6x + 9): This is also a perfect square trinomial, which can be factored as (x  3)^2.
The minus sign between the parentheses indicates subtraction.
Simplifying the Expression

Distribute the negative sign:
Since we are subtracting the entire second trinomial, we distribute the negative sign to each term inside the second parentheses. This gives us: (x^2 + 4x + 4)  x^2 + 6x  9 
Combine like terms: Now we combine the terms with the same variable and exponent: x^2  x^2 + 4x + 6x + 4  9

Simplify: This leaves us with the final simplified expression: 10x  5
Conclusion
By applying basic algebraic operations, we have successfully simplified the expression (x^2 + 4x + 4)  (x^2  6x + 9) to 10x  5. This simplified form is more concise and easier to work with in further calculations.