(2/3x-3/2x-1)^2 Expand

2 min read Jul 03, 2024

Expansion of (2/3x - 3/2x - 1)^2

In this article, we will learn how to expand the expression (2/3x - 3/2x - 1)^2. Expanding an expression like this can be a bit challenging, but with the right steps, you'll be able to do it easily.

Step 1: Simplify the Expression Inside the Parentheses

Before we expand the expression, let's simplify the expression inside the parentheses. We can do this by combining like terms.

2/3x - 3/2x - 1 = (4x - 9x)/6 - 1
              = (-5x)/6 - 1

So, the simplified expression is (-5x)/6 - 1.

Step 2: Expand the Expression

Now that we have simplified the expression inside the parentheses, we can expand the expression using the rule of exponentiation, which states that (a + b)^2 = a^2 + 2ab + b^2.

Let's apply this rule to our simplified expression:

((-5x)/6 - 1)^2 = ((-5x)/6)^2 + 2((-5x)/6)(-1) + (-1)^2

Step 3: Expand Each Term

Now, let's expand each term:

((-5x)/6)^2 = 25x^2/36
2((-5x)/6)(-1) = 10x/6
(-1)^2 = 1

Step 4: Combine the Terms

Finally, let's combine the terms:

((-5x)/6 - 1)^2 = 25x^2/36 + 10x/6 + 1

And that's the expanded expression!

The Final Answer

So, the expansion of (2/3x - 3/2x - 1)^2 is:

25x^2/36 + 10x/6 + 1

I hope this helps! Let me know if you have any questions or need further clarification.