(2x+3)3 Answer

2 min read Jul 03, 2024

(2x+3)³: A Simple Explanation and Solution

In this article, we will explore the solution to the expression (2x+3)³. This expression may seem daunting at first, but with a few simple steps, we can easily evaluate it.

What is the Cube of a Binomial?

Before we dive into the solution, let's quickly review what the cube of a binomial is. A binomial is an expression consisting of two terms, such as 2x+3. The cube of a binomial is when we raise the entire expression to the power of 3.

The Formula: (a+b)³

To evaluate the cube of a binomial, we can use the following formula:

(a+b)³ = a³ + 3a²b + 3ab² + b³

Applying the Formula to (2x+3)³

Now, let's apply this formula to our original expression:

(2x+3)³ = (2x)³ + 3(2x)²(3) + 3(2x)(3)² + (3)³

Simplifying the Expression

Next, we'll simplify each term:

(2x)³ = 8x³
3(2x)²(3) = 3(4x²)(3) = 36x²
3(2x)(3)² = 3(2x)(9) = 54x
(3)³ = 27

The Final Answer

Now, let's combine the simplified terms:

(2x+3)³ = 8x³ + 36x² + 54x + 27

And that's the final answer!

In conclusion, evaluating the expression (2x+3)³ is a straightforward process using the formula for the cube of a binomial. By applying the formula and simplifying the terms, we arrive at the final answer: 8x³ + 36x² + 54x + 27.