%5E2.jpeg "(x-12)^2")
Understanding (x-12)^2
(x-12)^2 is a mathematical expression that represents the square of the difference between x and 12. In simpler terms, it means multiplying the quantity (x-12) by itself.
Here's a breakdown:
1. Parentheses First:
- The parentheses indicate that we must perform the operation within them first. In this case, we subtract 12 from x.
2. Squaring:
- The exponent 2 means we multiply the result of (x-12) by itself.
Expanding the Expression
We can expand (x-12)^2 using the FOIL method (First, Outer, Inner, Last):
- First: x * x = x^2
- Outer: x * -12 = -12x
- Inner: -12 * x = -12x
- Last: -12 * -12 = 144
Combining the terms, we get:
(x-12)^2 = x^2 - 12x - 12x + 144
Simplifying the Expression:
Combining the like terms, we get the simplified form:
(x-12)^2 = x^2 - 24x + 144
Applications
This expression is widely used in various mathematical and scientific applications, including:
- Algebra: Solving quadratic equations and simplifying expressions.
- Calculus: Finding derivatives and integrals.
- Physics: Modelling motion and analyzing forces.
- Geometry: Calculating areas and volumes.
Key Points
- Parentheses matter: Remember to perform the operation inside the parentheses first.
- FOIL method: This method helps to expand squared expressions.
- Simplified form: The simplified form of (x-12)^2 is x^2 - 24x + 144.
By understanding the concept of squaring and expanding expressions, you can effectively work with (x-12)^2 and its various applications.