%5E3-in-expanded-form.jpeg "(x-2/3y)^3 In Expanded Form")
Cubing Binomials: (x-2/3y)^3 in Expanded Form
When working with algebraic expressions, it's essential to understand how to expand binomials raised to a power. In this article, we'll explore the process of expanding the binomial (x-2/3y)^3 and simplify the resulting expression.
** Binomial Expansion Formula **
To expand a binomial raised to a power, we can use the binomial expansion formula, which is given by:
(a+b)^n = a^n + na^(n-1)b + n(n-1)/2! a^(n-2)b^2 + … + b^n
where a and b are the two terms in the binomial, and n is the power to which it is raised.
** Expanding (x-2/3y)^3 **
Using the binomial expansion formula, we can expand (x-2/3y)^3 as follows:
(x-2/3y)^3 = x^3 + 3x^2(-2/3y) + 3x(-2/3y)^2 + (-2/3y)^3
** Simplifying the Expression **
Now, let's simplify each term in the expansion:
x^3
This term remains unchanged.
3x^2(-2/3y)
= -2x^2y
3x(-2/3y)^2
= 3x(-4/9y^2)
= -4xy^2/3
(-2/3y)^3
= -8y^3/27
** Final Expanded Form **
Combining the simplified terms, we get the expanded form of (x-2/3y)^3:
(x-2/3y)^3 = x^3 - 2x^2y - 4xy^2/3 - 8y^3/27
This is the desired expanded form of the binomial (x-2/3y)^3.
