Answer :
To find the sum of the given polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], follow these steps:
1. Identify the Like Terms:
- Look at the terms in each polynomial:
- The first polynomial is [tex]\(7x^3 - 4x^2\)[/tex].
- The second polynomial is [tex]\(2x^3 - 4x^2\)[/tex].
2. Combine the Coefficients of Like Terms:
- For the [tex]\(x^3\)[/tex] terms:
- Add the coefficients: [tex]\(7 + 2 = 9\)[/tex].
- So, the result for the [tex]\(x^3\)[/tex] terms is [tex]\(9x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms:
- Add the coefficients: [tex]\(-4 + (-4) = -8\)[/tex].
- So, the result for the [tex]\(x^2\)[/tex] terms is [tex]\(-8x^2\)[/tex].
3. Write the Resulting Polynomial:
- Combine the results from the like terms: [tex]\(9x^3 - 8x^2\)[/tex].
Therefore, the sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex]. This matches the option [tex]\(9x^3 - 8x^2\)[/tex] from the choices provided.
1. Identify the Like Terms:
- Look at the terms in each polynomial:
- The first polynomial is [tex]\(7x^3 - 4x^2\)[/tex].
- The second polynomial is [tex]\(2x^3 - 4x^2\)[/tex].
2. Combine the Coefficients of Like Terms:
- For the [tex]\(x^3\)[/tex] terms:
- Add the coefficients: [tex]\(7 + 2 = 9\)[/tex].
- So, the result for the [tex]\(x^3\)[/tex] terms is [tex]\(9x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms:
- Add the coefficients: [tex]\(-4 + (-4) = -8\)[/tex].
- So, the result for the [tex]\(x^2\)[/tex] terms is [tex]\(-8x^2\)[/tex].
3. Write the Resulting Polynomial:
- Combine the results from the like terms: [tex]\(9x^3 - 8x^2\)[/tex].
Therefore, the sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex]. This matches the option [tex]\(9x^3 - 8x^2\)[/tex] from the choices provided.
