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 terms involving [tex]\(x^3\)[/tex] are [tex]\(7x^3\)[/tex] and [tex]\(2x^3\)[/tex].
- The terms involving [tex]\(x^2\)[/tex] are [tex]\(-4x^2\)[/tex] and [tex]\(-4x^2\)[/tex].
2. Add the Coefficients of [tex]\(x^3\)[/tex] Terms:
- Add the coefficients of the [tex]\(x^3\)[/tex] terms: [tex]\(7 + 2 = 9\)[/tex].
- So, the combined term for [tex]\(x^3\)[/tex] becomes [tex]\(9x^3\)[/tex].
3. Add the Coefficients of [tex]\(x^2\)[/tex] Terms:
- Add the coefficients of the [tex]\(x^2\)[/tex] terms: [tex]\((-4) + (-4) = -8\)[/tex].
- So, the combined term for [tex]\(x^2\)[/tex] becomes [tex]\(-8x^2\)[/tex].
4. Write the Resulting Polynomial:
- Combine the results from the previous steps to form the sum of the polynomials: [tex]\(9x^3 - 8x^2\)[/tex].
Thus, the sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
1. Identify Like Terms:
- The terms involving [tex]\(x^3\)[/tex] are [tex]\(7x^3\)[/tex] and [tex]\(2x^3\)[/tex].
- The terms involving [tex]\(x^2\)[/tex] are [tex]\(-4x^2\)[/tex] and [tex]\(-4x^2\)[/tex].
2. Add the Coefficients of [tex]\(x^3\)[/tex] Terms:
- Add the coefficients of the [tex]\(x^3\)[/tex] terms: [tex]\(7 + 2 = 9\)[/tex].
- So, the combined term for [tex]\(x^3\)[/tex] becomes [tex]\(9x^3\)[/tex].
3. Add the Coefficients of [tex]\(x^2\)[/tex] Terms:
- Add the coefficients of the [tex]\(x^2\)[/tex] terms: [tex]\((-4) + (-4) = -8\)[/tex].
- So, the combined term for [tex]\(x^2\)[/tex] becomes [tex]\(-8x^2\)[/tex].
4. Write the Resulting Polynomial:
- Combine the results from the previous steps to form the sum of the polynomials: [tex]\(9x^3 - 8x^2\)[/tex].
Thus, the sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
