3-in-expanded-form.jpeg "(3/2x+1)3 In Expanded Form")
Expanding the Expression: (3/2x+1)3
In this article, we will discuss the expansion of the algebraic expression (3/2x+1)3 in its simplest form.
The Given Expression
The expression given is (3/2x+1)3, which is a cubic expression. To expand this expression, we need to follow the order of operations (PEMDAS) and multiply the binomial 3/2x+1 by itself three times.
Step 1: Multiply the Binomial by Itself
First, we will multiply the binomial 3/2x+1 by itself:
(3/2x+1)(3/2x+1)
Step 2: Multiply Again
Next, we will multiply the result by the binomial again:
(3/2x+1)(3/2x+1)(3/2x+1)
Expanding the Expression
Now, let's expand the expression by multiplying each term:
(3/2x+1)(3/2x+1)(3/2x+1) = (3/2x)^3 + 3(3/2x)^2(1) + 3(3/2x)(1)^2 + (1)^3
Simplifying the Expression
Simplifying the expression, we get:
(3/2x)^3 + (27/4)x^2 + (9/2)x + 1
The Expanded Form
Thus, the expanded form of the expression (3/2x+1)3 is:
(3/2x)^3 + (27/4)x^2 + (9/2)x + 1
In conclusion, we have successfully expanded the expression (3/2x+1)3 in its simplest form. This result can be used in various mathematical applications, such as solving equations and graphing functions.
