%5E3.jpeg "(x+2y)^3")
(x+2y)^3:Expansion and Simplification
In algebra, expanding powers of binomials is an essential skill. One such example is the expansion of (x+2y)^3. In this article, we will explore the process of expanding and simplifying this expression.
Expansion of (x+2y)^3
To expand (x+2y)^3, we can use the binomial theorem or the method of repeated multiplication. Here, we will use the latter method.
(x+2y)^3 = (x+2y)(x+2y)(x+2y)
We start by multiplying the first two factors:
(x+2y)(x+2y) = x^2 + 4xy + 4y^2
Now, we multiply the result by the third factor:
(x^2 + 4xy + 4y^2)(x+2y) = x^3 + 6x^2y + 12xy^2 + 8y^3
Thus, we have:
(x+2y)^3 = x^3 + 6x^2y + 12xy^2 + 8y^3
Simplification
The expanded form of (x+2y)^3 is already in its simplest form. There are no like terms to combine, and no common factors to cancel out.
Conclusion
In this article, we have expanded and simplified the expression (x+2y)^3. The final result is a polynomial of degree 3 with four terms: x^3, 6x^2y, 12xy^2, and 8y^3. This expansion and simplification process is a crucial skill in algebra and is used extensively in various mathematical and real-world applications.
