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.
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.
