(1-x)^2 Expand

Jasonbradley

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Jun 16, 2024

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Expanding (1-x)^2

The expression (1-x)^2 represents the square of the binomial (1-x). To expand this, we can apply the FOIL method or the square of a binomial formula.

Expanding using FOIL

FOIL stands for First, Outer, Inner, Last. This method helps us multiply two binomials:

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

Combining the terms, we get: 1 - x - x + x^2

Simplifying, the expanded form of (1-x)^2 is: 1 - 2x + x^2

Expanding using the Square of a Binomial Formula

The square of a binomial formula states: (a - b)^2 = a^2 - 2ab + b^2

Applying this formula to (1-x)^2, we have:

• a = 1
• b = x

Therefore, (1-x)^2 = 1^2 - 2(1)(x) + x^2

Simplifying, we again obtain: 1 - 2x + x^2

Conclusion

Both methods result in the same expanded form for (1-x)^2: 1 - 2x + x^2. Choosing which method to use depends on personal preference and the specific problem at hand. The FOIL method might be more intuitive for some, while the formula provides a more concise and efficient approach.