%5E3-expanded-form.jpeg "(x-1)^3 Expanded Form")
(x-1)^3 in Expanded Form
In algebra, expanding a binomial expression like (x-1)^3 means expressing it as a polynomial with individual terms. This article will guide you through the process of expanding (x-1)^3 and provide the final result.
What is Expanding (x-1)^3?
Expanding (x-1)^3 means expressing the cube of the binomial (x-1) as a sum of individual terms, each with a coefficient and a variable (x) raised to a certain power. This process involves multiplying the binomial by itself three times and then simplifying the resulting expression.
Expanding (x-1)^3 Using the Binomial Theorem
The binomial theorem provides a shortcut for expanding binomials raised to a power. The theorem states that:
(a+b)^n = a^n + na^(n-1)b + n(n-1)a^(n-2)b^2 + ... + nab^(n-1) + b^n
In our case, we have (x-1)^3, so we'll use the theorem with a = x and b = -1.
(x-1)^3 = x^3 + 3x^2(-1) + 3x(-1)^2 + (-1)^3
= x^3 - 3x^2 + 3x - 1
Expanded Form of (x-1)^3
The expanded form of (x-1)^3 is:
x^3 - 3x^2 + 3x - 1
This is the final result of expanding (x-1)^3. You can now use this expression for further algebraic manipulations or substitutions.
Conclusion
In this article, we have successfully expanded (x-1)^3 using the binomial theorem. The resulting expression is a cubic polynomial with four terms. Remember, expanding binomials is an essential skill in algebra, and the binomial theorem provides a powerful tool for doing so.
