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(x-1)^2 Simplify

2 min read Jun 17, 2024
(x-1)^2 Simplify

Simplifying (x-1)^2

The expression (x-1)^2 is a common algebraic expression that can be simplified using the concept of squaring a binomial.

Understanding the Concept

Squaring a binomial means multiplying the binomial by itself. In this case:

(x-1)^2 = (x-1) * (x-1)

Applying the FOIL Method

To simplify this, we can use the FOIL method, which stands for:

  • First: Multiply the first terms of each binomial (x * x = x^2)
  • Outer: Multiply the outer terms of the binomials (x * -1 = -x)
  • Inner: Multiply the inner terms of the binomials (-1 * x = -x)
  • Last: Multiply the last terms of each binomial (-1 * -1 = 1)

The Simplified Expression

Putting it all together:

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

Combining like terms:

** (x-1)^2 = x^2 - 2x + 1 **

Key Takeaways

  • Squaring a binomial: (a - b)^2 = a^2 - 2ab + b^2
  • FOIL method: a useful technique for multiplying binomials.
  • Simplifying: Combine like terms to obtain the final, simplified expression.

This simplified expression can be used for various algebraic manipulations and solving equations.

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