Answer :
To find the simplest form of the expression [tex]\((4x^3 + 6x - 7) + (3x^3 - 5x^2 - 5x)\)[/tex], follow these steps:
1. Combine Like Terms:
Start by identifying and combining the terms with the same degree (the same power of [tex]\(x\)[/tex]) from both polynomials.
- For [tex]\(x^3\)[/tex] terms:
- From the first polynomial: [tex]\(4x^3\)[/tex]
- From the second polynomial: [tex]\(3x^3\)[/tex]
- Combine them: [tex]\(4x^3 + 3x^3 = 7x^3\)[/tex]
- For [tex]\(x^2\)[/tex] terms:
- There are no [tex]\(x^2\)[/tex] terms in the first polynomial.
- From the second polynomial: [tex]\(-5x^2\)[/tex]
- So, the [tex]\(x^2\)[/tex] term is: [tex]\(-5x^2\)[/tex]
- For [tex]\(x\)[/tex] terms:
- From the first polynomial: [tex]\(6x\)[/tex]
- From the second polynomial: [tex]\(-5x\)[/tex]
- Combine them: [tex]\(6x - 5x = x\)[/tex]
- Constant terms:
- From the first polynomial: [tex]\(-7\)[/tex]
- There are no constant terms from the second polynomial.
- So, the constant term remains: [tex]\(-7\)[/tex]
2. Write the Simplified Polynomial:
After combining all the like terms, the simplest form of the expression is:
[tex]\[
7x^3 - 5x^2 + x - 7
\][/tex]
Hence, the answer is [tex]\(7x^3 - 5x^2 + x - 7\)[/tex].
1. Combine Like Terms:
Start by identifying and combining the terms with the same degree (the same power of [tex]\(x\)[/tex]) from both polynomials.
- For [tex]\(x^3\)[/tex] terms:
- From the first polynomial: [tex]\(4x^3\)[/tex]
- From the second polynomial: [tex]\(3x^3\)[/tex]
- Combine them: [tex]\(4x^3 + 3x^3 = 7x^3\)[/tex]
- For [tex]\(x^2\)[/tex] terms:
- There are no [tex]\(x^2\)[/tex] terms in the first polynomial.
- From the second polynomial: [tex]\(-5x^2\)[/tex]
- So, the [tex]\(x^2\)[/tex] term is: [tex]\(-5x^2\)[/tex]
- For [tex]\(x\)[/tex] terms:
- From the first polynomial: [tex]\(6x\)[/tex]
- From the second polynomial: [tex]\(-5x\)[/tex]
- Combine them: [tex]\(6x - 5x = x\)[/tex]
- Constant terms:
- From the first polynomial: [tex]\(-7\)[/tex]
- There are no constant terms from the second polynomial.
- So, the constant term remains: [tex]\(-7\)[/tex]
2. Write the Simplified Polynomial:
After combining all the like terms, the simplest form of the expression is:
[tex]\[
7x^3 - 5x^2 + x - 7
\][/tex]
Hence, the answer is [tex]\(7x^3 - 5x^2 + x - 7\)[/tex].
