Answer :
Let's go through the solution step-by-step to simplify the expression:
The problem asks us to perform the operations and simplify the expression [tex]\((6x^6 + 5x^3) + (9x^6 + 6x^3 + 4)\)[/tex].
1. Combine like terms:
- First, identify the like terms in the expression. These are terms that have the same variable raised to the same power.
- In [tex]\((6x^6 + 5x^3) + (9x^6 + 6x^3 + 4)\)[/tex], the like terms are:
- [tex]\(6x^6\)[/tex] and [tex]\(9x^6\)[/tex] (both are [tex]\(x^6\)[/tex] terms)
- [tex]\(5x^3\)[/tex] and [tex]\(6x^3\)[/tex] (both are [tex]\(x^3\)[/tex] terms)
- The constant term [tex]\(4\)[/tex] is on its own.
2. Add the coefficients of like terms:
- For the [tex]\(x^6\)[/tex] terms:
- [tex]\(6x^6 + 9x^6 = 15x^6\)[/tex]
- For the [tex]\(x^3\)[/tex] terms:
- [tex]\(5x^3 + 6x^3 = 11x^3\)[/tex]
- The constant term remains the same:
- [tex]\(4\)[/tex]
3. Write down the simplified expression:
- After combining all like terms, the simplified expression is:
[tex]\[ 15x^6 + 11x^3 + 4 \][/tex]
This is the simplified result of the given expression.
The problem asks us to perform the operations and simplify the expression [tex]\((6x^6 + 5x^3) + (9x^6 + 6x^3 + 4)\)[/tex].
1. Combine like terms:
- First, identify the like terms in the expression. These are terms that have the same variable raised to the same power.
- In [tex]\((6x^6 + 5x^3) + (9x^6 + 6x^3 + 4)\)[/tex], the like terms are:
- [tex]\(6x^6\)[/tex] and [tex]\(9x^6\)[/tex] (both are [tex]\(x^6\)[/tex] terms)
- [tex]\(5x^3\)[/tex] and [tex]\(6x^3\)[/tex] (both are [tex]\(x^3\)[/tex] terms)
- The constant term [tex]\(4\)[/tex] is on its own.
2. Add the coefficients of like terms:
- For the [tex]\(x^6\)[/tex] terms:
- [tex]\(6x^6 + 9x^6 = 15x^6\)[/tex]
- For the [tex]\(x^3\)[/tex] terms:
- [tex]\(5x^3 + 6x^3 = 11x^3\)[/tex]
- The constant term remains the same:
- [tex]\(4\)[/tex]
3. Write down the simplified expression:
- After combining all like terms, the simplified expression is:
[tex]\[ 15x^6 + 11x^3 + 4 \][/tex]
This is the simplified result of the given expression.
