%5E3-expand.jpeg "(3-x)^3 Expand")
Expanding the Expression (3-x)^3
In this article, we will explore the expansion of the expression (3-x)^3. This is a fundamental concept in algebra and is used extensively in various mathematical operations.
What is the Expansion of (3-x)^3?
To expand the expression (3-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 = 3 and b = -x. Substituting these values into the formula, we get:
(3-x)^3 = 3^3 - 3(3^2)x + 3(3)(3)x^2 - x^3
Simplifying the expression, we get:
(3-x)^3 = 27 - 27x + 27x^2 - x^3
Expanded Form of (3-x)^3
The expanded form of (3-x)^3 is:
27 - 27x + 27x^2 - x^3
This expression can be written in descending order of powers of x as:
- x^3 + 27x^2 - 27x + 27
Conclusion
In this article, we have successfully expanded the expression (3-x)^3 using the binomial theorem. The expanded form of the expression is - x^3 + 27x^2 - 27x + 27. This expansion is a crucial concept in algebra and is used extensively in various mathematical operations.
