Answer :
To find the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], follow these steps:
1. Identify Like Terms:
- The first polynomial is [tex]\(7x^3 - 4x^2\)[/tex].
- The second polynomial is [tex]\(2x^3 - 4x^2\)[/tex].
2. Add the [tex]\(x^3\)[/tex] Terms:
- From the first polynomial, the [tex]\(x^3\)[/tex] term is [tex]\(7x^3\)[/tex].
- From the second polynomial, the [tex]\(x^3\)[/tex] term is [tex]\(2x^3\)[/tex].
- Add these coefficients: [tex]\(7 + 2 = 9\)[/tex].
- So, the [tex]\(x^3\)[/tex] term in the sum is [tex]\(9x^3\)[/tex].
3. Add the [tex]\(x^2\)[/tex] Terms:
- From the first polynomial, the [tex]\(x^2\)[/tex] term is [tex]\(-4x^2\)[/tex].
- From the second polynomial, the [tex]\(x^2\)[/tex] term is also [tex]\(-4x^2\)[/tex].
- Add these coefficients: [tex]\(-4 + (-4) = -8\)[/tex].
- So, the [tex]\(x^2\)[/tex] term in the sum is [tex]\(-8x^2\)[/tex].
4. Write the Resulting Polynomial:
- Combine the results from steps 2 and 3: [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].
1. Identify Like Terms:
- The first polynomial is [tex]\(7x^3 - 4x^2\)[/tex].
- The second polynomial is [tex]\(2x^3 - 4x^2\)[/tex].
2. Add the [tex]\(x^3\)[/tex] Terms:
- From the first polynomial, the [tex]\(x^3\)[/tex] term is [tex]\(7x^3\)[/tex].
- From the second polynomial, the [tex]\(x^3\)[/tex] term is [tex]\(2x^3\)[/tex].
- Add these coefficients: [tex]\(7 + 2 = 9\)[/tex].
- So, the [tex]\(x^3\)[/tex] term in the sum is [tex]\(9x^3\)[/tex].
3. Add the [tex]\(x^2\)[/tex] Terms:
- From the first polynomial, the [tex]\(x^2\)[/tex] term is [tex]\(-4x^2\)[/tex].
- From the second polynomial, the [tex]\(x^2\)[/tex] term is also [tex]\(-4x^2\)[/tex].
- Add these coefficients: [tex]\(-4 + (-4) = -8\)[/tex].
- So, the [tex]\(x^2\)[/tex] term in the sum is [tex]\(-8x^2\)[/tex].
4. Write the Resulting Polynomial:
- Combine the results from steps 2 and 3: [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].
