%5E4-expand.jpeg "(x-1)^4 Expand")
Expanding (x-1)^4
The expression (x-1)^4 represents the fourth power of the binomial (x-1). To expand this expression, we can use the Binomial Theorem.
The Binomial Theorem
The Binomial Theorem provides a general formula for expanding any binomial raised to a positive integer power:
(a + b)^n = a^n + na^(n-1)b + (n(n-1)/2!)a^(n-2)b^2 + ... + nb^(n-1)a + b^n
where n is a positive integer, and n! denotes the factorial of n.
Expanding (x-1)^4
Using the Binomial Theorem, we can expand (x-1)^4 as follows:
(x - 1)^4 = x^4 + 4x^3(-1) + 6x^2(-1)^2 + 4x(-1)^3 + (-1)^4
Simplifying the terms, we get:
(x - 1)^4 = x^4 - 4x^3 + 6x^2 - 4x + 1
Conclusion
Therefore, the expanded form of (x-1)^4 is x^4 - 4x^3 + 6x^2 - 4x + 1. This can be achieved by applying the Binomial Theorem and simplifying the resulting terms.