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**Part 2: Combine Like Terms**

**Question 1:** Simplify the following expression:

[tex]\[ 45x^3 + 2 \][/tex]

A. [tex]\( 45x^5 - 14x^2 \)[/tex]

B. [tex]\( -15 \)[/tex]

C. [tex]\( 4x^8 \)[/tex]

D. [tex]\( 45x^3 + 2 \)[/tex]

Answer :

Sure, let's walk through the question step by step to combine like terms in the given expressions.

We are given two polynomial expressions:

1. [tex]\( 45x^3 + 2 \)[/tex]
2. [tex]\( 4.45x^5 - 14x^2 - 15 + 4x^8 \)[/tex]

### Step 1: Analyze the given polynomials
- In the first polynomial [tex]\( 45x^3 + 2 \)[/tex], there are no like terms to combine because it consists of a term with [tex]\( x^3 \)[/tex] and a constant term.

### Step 2: Simplify the first polynomial
Since the first polynomial [tex]\( 45x^3 + 2 \)[/tex] has no like terms to combine, it remains as it is:

[tex]\[ 45x^3 + 2 \][/tex]

### Step 3: Analyze the second polynomial
- The second polynomial [tex]\( 4.45x^5 - 14x^2 - 15 + 4x^8 \)[/tex] also has no like terms. Each term has a unique power of [tex]\( x \)[/tex].

### Step 4: Simplify the second polynomial
Since there are no like terms in the second polynomial as well, it remains the same:

[tex]\[ 4x^8 + 4.45x^5 - 14x^2 - 15 \][/tex]

### Final Simplified Expressions

1. The simplified first polynomial:
[tex]\[ 45x^3 + 2 \][/tex]

2. The simplified second polynomial:
[tex]\[ 4x^8 + 4.45x^5 - 14x^2 - 15 \][/tex]

These are the simplified forms of the given polynomials, and since there were no like terms in each polynomial, they both remain unchanged.

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