%5E3-expanded.jpeg "(1-x)^3 Expanded")
Expanded Form of (1-x)^3
In algebra, one of the most common operations is exponentiation, where a number or expression is raised to a certain power. In this article, we will explore the expanded form of (1-x)^3, a cubic expression.
What is (1-x)^3?
The expression (1-x)^3 is a cubic expression, where the base is (1-x) and the exponent is 3. This means that we need to raise (1-x) to the power of 3.
Expanded Form using Binomial Theorem
To expand (1-x)^3, we can use the Binomial Theorem, which states that:
(a+b)^n = a^n + na^(n-1)b + n(n-1)a^(n-2)b^2 + ... + b^n
In this case, we have a = 1 and b = -x. Substituting these values into the Binomial Theorem, we get:
(1-x)^3 = 1^3 + 3(1)^2(-x) + 3(1)(-x)^2 + (-x)^3
Simplifying the Expression
Now, let's simplify the expression by evaluating each term:
- 1^3 = 1
- 3(1)^2(-x) = -3x
- 3(1)(-x)^2 = 3x^2
- (-x)^3 = -x^3
Substituting these values back into the expression, we get:
(1-x)^3 = 1 - 3x + 3x^2 - x^3
Conclusion
In conclusion, the expanded form of (1-x)^3 is 1 - 3x + 3x^2 - x^3. This expression can be used in various mathematical operations, such as simplifying expressions or solving equations.
