Answer :
To find the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], let's add the corresponding terms step by step:
1. Handle the [tex]\(x^3\)[/tex] terms:
- First polynomial has [tex]\(7x^3\)[/tex].
- Second polynomial has [tex]\(2x^3\)[/tex].
- Add these coefficients: [tex]\(7 + 2 = 9\)[/tex].
So, the [tex]\(x^3\)[/tex] term in the resulting polynomial is [tex]\(9x^3\)[/tex].
2. Handle the [tex]\(x^2\)[/tex] terms:
- First polynomial has [tex]\(-4x^2\)[/tex].
- Second polynomial has [tex]\(-4x^2\)[/tex].
- Add these coefficients: [tex]\(-4 + (-4) = -8\)[/tex].
So, the [tex]\(x^2\)[/tex] term in the resulting polynomial is [tex]\(-8x^2\)[/tex].
3. Combine the results:
- Combine the [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex] terms to form the sum of the polynomials: [tex]\(9x^3 - 8x^2\)[/tex].
Thus, the sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
1. Handle the [tex]\(x^3\)[/tex] terms:
- First polynomial has [tex]\(7x^3\)[/tex].
- Second polynomial has [tex]\(2x^3\)[/tex].
- Add these coefficients: [tex]\(7 + 2 = 9\)[/tex].
So, the [tex]\(x^3\)[/tex] term in the resulting polynomial is [tex]\(9x^3\)[/tex].
2. Handle the [tex]\(x^2\)[/tex] terms:
- First polynomial has [tex]\(-4x^2\)[/tex].
- Second polynomial has [tex]\(-4x^2\)[/tex].
- Add these coefficients: [tex]\(-4 + (-4) = -8\)[/tex].
So, the [tex]\(x^2\)[/tex] term in the resulting polynomial is [tex]\(-8x^2\)[/tex].
3. Combine the results:
- Combine the [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex] terms to form the sum of the polynomials: [tex]\(9x^3 - 8x^2\)[/tex].
Thus, the sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
