Answer :
To find the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], we start by adding the like terms. Here is the step-by-step solution:
1. Identify the like terms:
- The terms with [tex]\(x^3\)[/tex] are [tex]\(7x^3\)[/tex] from the first polynomial and [tex]\(2x^3\)[/tex] from the second polynomial.
- The terms with [tex]\(x^2\)[/tex] are [tex]\(-4x^2\)[/tex] from both polynomials.
2. Add the coefficients of the like terms:
- For the [tex]\(x^3\)[/tex] terms: [tex]\(7 + 2 = 9\)[/tex]. This gives us [tex]\(9x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms: [tex]\(-4 + (-4) = -8\)[/tex]. This gives us [tex]\(-8x^2\)[/tex].
3. Combine the results:
- The sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
Therefore, the correct sum is [tex]\(\boxed{9x^3 - 8x^2}\)[/tex].
1. Identify the like terms:
- The terms with [tex]\(x^3\)[/tex] are [tex]\(7x^3\)[/tex] from the first polynomial and [tex]\(2x^3\)[/tex] from the second polynomial.
- The terms with [tex]\(x^2\)[/tex] are [tex]\(-4x^2\)[/tex] from both polynomials.
2. Add the coefficients of the like terms:
- For the [tex]\(x^3\)[/tex] terms: [tex]\(7 + 2 = 9\)[/tex]. This gives us [tex]\(9x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms: [tex]\(-4 + (-4) = -8\)[/tex]. This gives us [tex]\(-8x^2\)[/tex].
3. Combine the results:
- The sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
Therefore, the correct sum is [tex]\(\boxed{9x^3 - 8x^2}\)[/tex].
