Answer :
To find the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], we'll combine like terms from each polynomial.
1. Combine the [tex]\(x^3\)[/tex] terms:
- The first polynomial has [tex]\(7x^3\)[/tex].
- The second polynomial has [tex]\(2x^3\)[/tex].
- Adding these together: [tex]\(7x^3 + 2x^3 = 9x^3\)[/tex].
2. Combine the [tex]\(x^2\)[/tex] terms:
- The first polynomial has [tex]\(-4x^2\)[/tex].
- The second polynomial also has [tex]\(-4x^2\)[/tex].
- Adding these together: [tex]\(-4x^2 + (-4x^2) = -8x^2\)[/tex].
Now, we combine the results from the above steps to get the final sum of the polynomials:
- Combine the [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex] terms: [tex]\(9x^3 - 8x^2\)[/tex].
So, the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex] is [tex]\(9x^3 - 8x^2\)[/tex].
Therefore, the correct answer is [tex]\(9x^3 - 8x^2\)[/tex], which corresponds to the choice [tex]\(9x^3 - 8x^2\)[/tex].
1. Combine the [tex]\(x^3\)[/tex] terms:
- The first polynomial has [tex]\(7x^3\)[/tex].
- The second polynomial has [tex]\(2x^3\)[/tex].
- Adding these together: [tex]\(7x^3 + 2x^3 = 9x^3\)[/tex].
2. Combine the [tex]\(x^2\)[/tex] terms:
- The first polynomial has [tex]\(-4x^2\)[/tex].
- The second polynomial also has [tex]\(-4x^2\)[/tex].
- Adding these together: [tex]\(-4x^2 + (-4x^2) = -8x^2\)[/tex].
Now, we combine the results from the above steps to get the final sum of the polynomials:
- Combine the [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex] terms: [tex]\(9x^3 - 8x^2\)[/tex].
So, the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex] is [tex]\(9x^3 - 8x^2\)[/tex].
Therefore, the correct answer is [tex]\(9x^3 - 8x^2\)[/tex], which corresponds to the choice [tex]\(9x^3 - 8x^2\)[/tex].
