(x-12)^2

2 min read Jun 17, 2024
(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.

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