Answer :
To find the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], we need to add corresponding terms from both polynomials.
Here is a step-by-step breakdown:
1. Identify Like Terms:
- Both polynomials have terms in [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex].
2. Add the [tex]\(x^3\)[/tex] Terms:
- The first polynomial has [tex]\(7x^3\)[/tex].
- The second polynomial has [tex]\(2x^3\)[/tex].
- Sum these terms: [tex]\(7x^3 + 2x^3 = 9x^3\)[/tex].
3. Add the [tex]\(x^2\)[/tex] Terms:
- The first polynomial has [tex]\(-4x^2\)[/tex].
- The second polynomial also has [tex]\(-4x^2\)[/tex].
- Sum these terms: [tex]\(-4x^2 + (-4x^2) = -8x^2\)[/tex].
4. Combine the Results:
- The resulting polynomial is [tex]\(9x^3 - 8x^2\)[/tex].
Therefore, the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex] is [tex]\(\boxed{9x^3 - 8x^2}\)[/tex].
Here is a step-by-step breakdown:
1. Identify Like Terms:
- Both polynomials have terms in [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex].
2. Add the [tex]\(x^3\)[/tex] Terms:
- The first polynomial has [tex]\(7x^3\)[/tex].
- The second polynomial has [tex]\(2x^3\)[/tex].
- Sum these terms: [tex]\(7x^3 + 2x^3 = 9x^3\)[/tex].
3. Add the [tex]\(x^2\)[/tex] Terms:
- The first polynomial has [tex]\(-4x^2\)[/tex].
- The second polynomial also has [tex]\(-4x^2\)[/tex].
- Sum these terms: [tex]\(-4x^2 + (-4x^2) = -8x^2\)[/tex].
4. Combine the Results:
- The resulting polynomial is [tex]\(9x^3 - 8x^2\)[/tex].
Therefore, the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex] is [tex]\(\boxed{9x^3 - 8x^2}\)[/tex].
