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(x-6)^2 Expand

2 min read Jun 17, 2024
(x-6)^2 Expand

Expanding (x-6)^2

Expanding a squared binomial like (x-6)^2 can be done using the FOIL method or by recognizing the square of a difference pattern.

Using FOIL Method

FOIL stands for First, Outer, Inner, Last. This method helps to multiply each term in the first binomial by each term in the second binomial.

  1. First: Multiply the first terms of each binomial: x * x = x^2
  2. Outer: Multiply the outer terms of each binomial: x * -6 = -6x
  3. Inner: Multiply the inner terms of each binomial: -6 * x = -6x
  4. Last: Multiply the last terms of each binomial: -6 * -6 = 36

Now, add all the terms together: x^2 - 6x - 6x + 36

Finally, combine like terms: x^2 - 12x + 36

Using the Square of a Difference Pattern

The square of a difference pattern states that (a - b)^2 = a^2 - 2ab + b^2

  1. Square the first term: x^2
  2. Multiply the two terms and double the result: 2 * x * -6 = -12x
  3. Square the second term: (-6)^2 = 36

Combine the results: x^2 - 12x + 36

Therefore, the expanded form of (x-6)^2 is x^2 - 12x + 36.

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