College

Collect like terms and then arrange them in descending order.

[tex]
\[
-x + \frac{3}{4} + 73x^9 - x - \frac{1}{2} - 3x^9
\]
[/tex]

Simplify the expression:

[tex]
\[
= (73x^9 - 3x^9) + (-x - x) + \left(\frac{3}{4} - \frac{1}{2}\right)
\]
[/tex]

Combine like terms:

[tex]
\[
= 70x^9 - 2x + \frac{1}{4}
\]
[/tex]

Final expression:

[tex]
\[
70x^9 - 2x + \frac{1}{4}
\]
[/tex]

Answer :

Let's simplify and collect like terms for the given expression:

The expression is:

[tex]\[
-x + \frac{3}{4} + 73x^9 - x - \frac{1}{2} - 3x^9
\][/tex]

Step 1: Combine like terms

1. Identify like terms:

- The terms involving [tex]\( x^9 \)[/tex] are [tex]\( 73x^9 \)[/tex] and [tex]\( -3x^9 \)[/tex].
- The terms involving [tex]\( x \)[/tex] are [tex]\( -x \)[/tex] and [tex]\( -x \)[/tex].
- The constant terms are [tex]\( \frac{3}{4} \)[/tex] and [tex]\( -\frac{1}{2} \)[/tex].

2. Combine each group of like terms:

- For the [tex]\( x^9 \)[/tex] terms:
- [tex]\( 73x^9 - 3x^9 = 70x^9 \)[/tex]
- For the [tex]\( x \)[/tex] terms:
- [tex]\(-x - x = -2x \)[/tex]
- For the constant terms:
- [tex]\(\frac{3}{4} - \frac{1}{2} = \frac{3}{4} - \frac{2}{4} = \frac{1}{4}\)[/tex]

Step 2: Write the expression in descending order of exponents

After combining the like terms, the simplified expression is:

[tex]\[
70x^9 - 2x + \frac{1}{4}
\][/tex]

This expression is already arranged in descending order of its exponents, from the highest degree term [tex]\( 70x^9 \)[/tex] to the constant term [tex]\( \frac{1}{4} \)[/tex].

Thus, the simplified and arranged expression is:

[tex]\[
70x^9 - 2x + \frac{1}{4}
\][/tex]