2-(x%2B3)(x-3).jpeg "(x-1)2-(x+3)(x-3)")
Simplifying the Expression: $(x-1)^2 - (x+3)(x-3)$
In this article, we will simplify the algebraic expression $(x-1)^2 - (x+3)(x-3)$. To do this, we will follow the order of operations (PEMDAS) and apply the distributive property.
Step 1: Expand the Square
First, we will expand the square term $(x-1)^2$ using the formula $(a-b)^2 = a^2 - 2ab + b^2$.
$(x-1)^2 = x^2 - 2x + 1$
Step 2: Expand the Product
Next, we will expand the product $(x+3)(x-3)$ using the distributive property.
$(x+3)(x-3) = x^2 - 9$
Step 3: Simplify the Expression
Now, we will substitute the expanded expressions into the original equation.
$(x-1)^2 - (x+3)(x-3) = (x^2 - 2x + 1) - (x^2 - 9)$
Step 4: Combine Like Terms
Finally, we will combine like terms to simplify the expression.
$(x^2 - 2x + 1) - (x^2 - 9) = -2x + 10$
Conclusion
The simplified expression is $-2x + 10$. This result can be used for further calculations or analysis in various mathematical or real-world applications.
