Answer :
To find the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], follow these steps:
1. Identify Like Terms: The polynomials given are [tex]\(7x^3 - 4x^2\)[/tex] and [tex]\(2x^3 - 4x^2\)[/tex]. Notice that both polynomials have terms with [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex].
2. Add the Coefficients of the Like Terms:
- For the [tex]\(x^3\)[/tex] terms:
- You have [tex]\(7x^3\)[/tex] from the first polynomial and [tex]\(2x^3\)[/tex] from the second polynomial.
- Add these coefficients: [tex]\(7 + 2 = 9\)[/tex].
- This gives you [tex]\(9x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms:
- You have [tex]\(-4x^2\)[/tex] from both the first and the second polynomial.
- Add these coefficients: [tex]\(-4 + (-4) = -8\)[/tex].
- This gives you [tex]\(-8x^2\)[/tex].
3. Write the Resulting Polynomial:
- Combine the results from steps 2:
- You have [tex]\(9x^3\)[/tex] from the added [tex]\(x^3\)[/tex] terms and [tex]\(-8x^2\)[/tex] from the added [tex]\(x^2\)[/tex] terms.
The sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
This matches the option [tex]\(9x^3 - 8x^2\)[/tex].
1. Identify Like Terms: The polynomials given are [tex]\(7x^3 - 4x^2\)[/tex] and [tex]\(2x^3 - 4x^2\)[/tex]. Notice that both polynomials have terms with [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex].
2. Add the Coefficients of the Like Terms:
- For the [tex]\(x^3\)[/tex] terms:
- You have [tex]\(7x^3\)[/tex] from the first polynomial and [tex]\(2x^3\)[/tex] from the second polynomial.
- Add these coefficients: [tex]\(7 + 2 = 9\)[/tex].
- This gives you [tex]\(9x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms:
- You have [tex]\(-4x^2\)[/tex] from both the first and the second polynomial.
- Add these coefficients: [tex]\(-4 + (-4) = -8\)[/tex].
- This gives you [tex]\(-8x^2\)[/tex].
3. Write the Resulting Polynomial:
- Combine the results from steps 2:
- You have [tex]\(9x^3\)[/tex] from the added [tex]\(x^3\)[/tex] terms and [tex]\(-8x^2\)[/tex] from the added [tex]\(x^2\)[/tex] terms.
The sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
This matches the option [tex]\(9x^3 - 8x^2\)[/tex].
