24^2 -10x -21/32^2 -18

I have a feeling you have typos here.

Is that supposed to be 24x^2 at the top and 32x^2 ... at the bottom ?

yes

Just visit calc101.com and click on the long division button. Enter your expressions and see all the details.

Polynomial division is just like regular numeric long division, except that each column represents a power of x, not a power of 10.

You can play around with polynomial division till you feel comfortable doing it yourself.

To simplify the given expression, we can follow the order of operations (also known as PEMDAS/BODMAS) which stands for Parentheses/Brackets, Exponents/Orders, Multiplication/Division, and Addition/Subtraction. Let's break it down step by step:

Step 1: Evaluate exponents
We start by evaluating any exponents in the expression. In this case, we have 24^2 and 32^2:

24^2 = 24 * 24 = 576
32^2 = 32 * 32 = 1024

Now the expression becomes:

576 - 10x - 21/1024 - 18

Step 2: Perform multiplication and division
Next, we perform any multiplication and division from left to right in the expression. We have -21/1024, which is division.

The expression becomes:

576 - 10x - 0.0205078125 - 18

Step 3: Perform addition and subtraction
Lastly, we perform the addition and subtraction from left to right in the expression.

The simplified expression is:

558.9794921875 - 10x

So, the simplified expression is 558.9794921875 - 10x.