%5E2.jpeg "(x-11)^2")
Understanding (x-11)^2
The expression (x-11)^2 is a common mathematical term that represents the square of the binomial (x-11). Understanding this expression involves understanding the concept of squaring a binomial and how to expand it.
Expanding the Expression
To expand (x-11)^2, we can use the following formula:
(a - b)^2 = a^2 - 2ab + b^2
In this case, a = x and b = 11. Substituting these values into the formula, we get:
(x - 11)^2 = x^2 - 2(x)(11) + 11^2
Simplifying the expression:
** (x - 11)^2 = x^2 - 22x + 121**
Applications of (x-11)^2
The expression (x-11)^2 can be used in various mathematical contexts, including:
- Algebraic Manipulation: This expression can be used to solve equations, simplify expressions, and factor polynomials.
- Quadratic Equations: When set equal to zero, the expression represents a quadratic equation. The solutions to this equation can be found by using the quadratic formula.
- Graphing Functions: The expression can be used to graph a parabola, which is the shape of the graph of a quadratic function.
Conclusion
Understanding the expansion of (x-11)^2 is essential for working with algebraic expressions, solving equations, and understanding the behavior of quadratic functions. This expression provides a fundamental building block for more complex mathematical concepts.