%5E3-expanded.jpeg "(2x-3)^3 Expanded")
Expanding (2x-3)^3
In algebra, expanding an expression means to simplify it by removing any parentheses or combining like terms. In this article, we will learn how to expand the expression (2x-3)^3.
What is the Cube of a Binomial?
Before we dive into expanding (2x-3)^3, let's recall what the cube of a binomial is. A binomial is an expression consisting of two terms, such as 2x and -3. The cube of a binomial is the result of multiplying the binomial by itself three times.
Using the Binomial Theorem
To expand (2x-3)^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
where a and b are the terms of the binomial, and n is the power to which the binomial is raised.
In our case, a = 2x, b = -3, and n = 3. Substituting these values into the Binomial Theorem, we get:
(2x-3)^3 = (2x)^3 - 3(2x)^2(-3) + 3(2x)(-3)^2 - (-3)^3
Expanding the Expression
Now, let's expand each term of the expression:
(2x)^3 = 8x^3
-3(2x)^2(-3) = -3(4x^2)(-3) = 36x^2
3(2x)(-3)^2 = 3(2x)(9) = 54x
(-3)^3 = -27
Combining Like Terms
Finally, we can combine like terms to get the final expanded expression:
(2x-3)^3 = 8x^3 + 36x^2 + 54x - 27
And that's it! We have successfully expanded the expression (2x-3)^3.
