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(x-12)^2 In Standard Form

2 min read Jun 17, 2024
(x-12)^2 In Standard Form

Expanding and Simplifying (x-12)^2 to Standard Form

The expression (x-12)^2 represents the square of a binomial, and to write it in standard form, we need to expand and simplify it. Here's how:

Understanding the Concept

Standard form for a quadratic expression is ax^2 + bx + c, where 'a', 'b', and 'c' are constants.

To expand (x-12)^2, we can use the FOIL method or simply recognize it as a perfect square trinomial:

  • FOIL Method:

    • (x-12)(x-12)
    • x(x-12) - 12(x-12)
    • x^2 - 12x - 12x + 144
    • x^2 - 24x + 144

  • Perfect Square Trinomial:

    • (a-b)^2 = a^2 - 2ab + b^2
    • In this case, a = x and b = 12.
    • Therefore, (x-12)^2 = x^2 - 2(x)(12) + 12^2 = x^2 - 24x + 144

The Result

Both methods lead to the same result: (x-12)^2 = x^2 - 24x + 144

This is the standard form of the expression. We can see that:

  • a = 1
  • b = -24
  • c = 144

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