Answer :
To find the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], let's break down the steps:
1. Identify the Like Terms:
- In the expression, [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], the first polynomial is [tex]\(7x^3 - 4x^2\)[/tex] and the second polynomial is [tex]\(2x^3 - 4x^2\)[/tex].
- We have terms with [tex]\(x^3\)[/tex] and terms with [tex]\(x^2\)[/tex].
2. Add the [tex]\(x^3\)[/tex] Terms:
- From both polynomials, add the [tex]\(x^3\)[/tex] terms: [tex]\(7x^3 + 2x^3 = 9x^3\)[/tex].
3. Add the [tex]\(x^2\)[/tex] Terms:
- Similarly, add the [tex]\(x^2\)[/tex] terms: [tex]\(-4x^2 - 4x^2 = -8x^2\)[/tex].
4. Combine the Results:
- Combine the results from the like terms to form the sum of the polynomials: [tex]\(9x^3 - 8x^2\)[/tex].
Therefore, the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex] is [tex]\(9x^3 - 8x^2\)[/tex]. This corresponds to the choice [tex]\(9x^3 - 8x^2\)[/tex].
1. Identify the Like Terms:
- In the expression, [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], the first polynomial is [tex]\(7x^3 - 4x^2\)[/tex] and the second polynomial is [tex]\(2x^3 - 4x^2\)[/tex].
- We have terms with [tex]\(x^3\)[/tex] and terms with [tex]\(x^2\)[/tex].
2. Add the [tex]\(x^3\)[/tex] Terms:
- From both polynomials, add the [tex]\(x^3\)[/tex] terms: [tex]\(7x^3 + 2x^3 = 9x^3\)[/tex].
3. Add the [tex]\(x^2\)[/tex] Terms:
- Similarly, add the [tex]\(x^2\)[/tex] terms: [tex]\(-4x^2 - 4x^2 = -8x^2\)[/tex].
4. Combine the Results:
- Combine the results from the like terms to form the sum of the polynomials: [tex]\(9x^3 - 8x^2\)[/tex].
Therefore, the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex] is [tex]\(9x^3 - 8x^2\)[/tex]. This corresponds to the choice [tex]\(9x^3 - 8x^2\)[/tex].
