-(x%5E2-6x%2B9).jpeg "(x^2+4x+4)-(x^2-6x+9)")
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
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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
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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.