Answer :
To find the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], we will add the coefficients of the like terms:
1. Identify like terms:
- The terms with [tex]\(x^3\)[/tex] are [tex]\(7x^3\)[/tex] and [tex]\(2x^3\)[/tex].
- The terms with [tex]\(x^2\)[/tex] are [tex]\(-4x^2\)[/tex] and [tex]\(-4x^2\)[/tex].
2. Add the coefficients of the [tex]\(x^3\)[/tex] terms:
- [tex]\(7\)[/tex] (from [tex]\(7x^3\)[/tex]) plus [tex]\(2\)[/tex] (from [tex]\(2x^3\)[/tex]) gives us [tex]\(9x^3\)[/tex].
3. Add the coefficients of the [tex]\(x^2\)[/tex] terms:
- [tex]\(-4\)[/tex] (from [tex]\(-4x^2\)[/tex]) plus [tex]\(-4\)[/tex] (from [tex]\(-4x^2\)[/tex]) gives us [tex]\(-8x^2\)[/tex].
4. Combine the results:
- The polynomial sum is [tex]\(9x^3 - 8x^2\)[/tex].
Therefore, the sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
1. Identify like terms:
- The terms with [tex]\(x^3\)[/tex] are [tex]\(7x^3\)[/tex] and [tex]\(2x^3\)[/tex].
- The terms with [tex]\(x^2\)[/tex] are [tex]\(-4x^2\)[/tex] and [tex]\(-4x^2\)[/tex].
2. Add the coefficients of the [tex]\(x^3\)[/tex] terms:
- [tex]\(7\)[/tex] (from [tex]\(7x^3\)[/tex]) plus [tex]\(2\)[/tex] (from [tex]\(2x^3\)[/tex]) gives us [tex]\(9x^3\)[/tex].
3. Add the coefficients of the [tex]\(x^2\)[/tex] terms:
- [tex]\(-4\)[/tex] (from [tex]\(-4x^2\)[/tex]) plus [tex]\(-4\)[/tex] (from [tex]\(-4x^2\)[/tex]) gives us [tex]\(-8x^2\)[/tex].
4. Combine the results:
- The polynomial sum is [tex]\(9x^3 - 8x^2\)[/tex].
Therefore, the sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
