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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]
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]
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