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(x-2)^2 Foil

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

Understanding FOIL: Expanding (x-2)^2

The FOIL method is a handy tool for expanding binomials (expressions with two terms). Let's use it to expand the expression (x-2)^2.

What is FOIL?

FOIL stands for First, Outer, Inner, Last. It's a mnemonic device to help you remember the order to multiply terms when expanding binomials:

  1. First: Multiply the first terms of each binomial.
  2. Outer: Multiply the outer terms of the binomials.
  3. Inner: Multiply the inner terms of the binomials.
  4. Last: Multiply the last terms of each binomial.

Applying FOIL to (x-2)^2

Since (x-2)^2 is the same as (x-2)(x-2), let's apply FOIL:

  1. First: x * x = x^2
  2. Outer: x * -2 = -2x
  3. Inner: -2 * x = -2x
  4. Last: -2 * -2 = 4

Now, combine the terms:

x^2 - 2x - 2x + 4

Simplify by combining like terms:

x^2 - 4x + 4

Conclusion

Therefore, (x-2)^2 expanded using the FOIL method is x^2 - 4x + 4. Remember, FOIL is a simple but powerful tool for expanding binomials.

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