Answer :
To find the sum of the polynomials [tex]\((7x^3 - 4x^2)\)[/tex] and [tex]\((2x^3 - 4x^2)\)[/tex], follow these steps:
1. Identify Like Terms:
- The first polynomial, [tex]\(7x^3 - 4x^2\)[/tex], has terms [tex]\(7x^3\)[/tex] and [tex]\(-4x^2\)[/tex].
- The second polynomial, [tex]\(2x^3 - 4x^2\)[/tex], has terms [tex]\(2x^3\)[/tex] and [tex]\(-4x^2\)[/tex].
2. Add the Like Terms:
- Combine the cubic terms: [tex]\(7x^3\)[/tex] from the first polynomial and [tex]\(2x^3\)[/tex] from the second polynomial. Adding these gives [tex]\(7x^3 + 2x^3 = 9x^3\)[/tex].
- Combine the quadratic terms: [tex]\(-4x^2\)[/tex] from the first polynomial and [tex]\(-4x^2\)[/tex] from the second polynomial. Adding these gives [tex]\(-4x^2 + (-4x^2) = -8x^2\)[/tex].
3. Write the Resulting Polynomial:
- The sum of the polynomials is the sum of the combined like terms. Therefore, the resulting polynomial is [tex]\(9x^3 - 8x^2\)[/tex].
Thus, the sum of the polynomials [tex]\((7x^3 - 4x^2)\)[/tex] and [tex]\((2x^3 - 4x^2)\)[/tex] is [tex]\(9x^3 - 8x^2\)[/tex].
1. Identify Like Terms:
- The first polynomial, [tex]\(7x^3 - 4x^2\)[/tex], has terms [tex]\(7x^3\)[/tex] and [tex]\(-4x^2\)[/tex].
- The second polynomial, [tex]\(2x^3 - 4x^2\)[/tex], has terms [tex]\(2x^3\)[/tex] and [tex]\(-4x^2\)[/tex].
2. Add the Like Terms:
- Combine the cubic terms: [tex]\(7x^3\)[/tex] from the first polynomial and [tex]\(2x^3\)[/tex] from the second polynomial. Adding these gives [tex]\(7x^3 + 2x^3 = 9x^3\)[/tex].
- Combine the quadratic terms: [tex]\(-4x^2\)[/tex] from the first polynomial and [tex]\(-4x^2\)[/tex] from the second polynomial. Adding these gives [tex]\(-4x^2 + (-4x^2) = -8x^2\)[/tex].
3. Write the Resulting Polynomial:
- The sum of the polynomials is the sum of the combined like terms. Therefore, the resulting polynomial is [tex]\(9x^3 - 8x^2\)[/tex].
Thus, the sum of the polynomials [tex]\((7x^3 - 4x^2)\)[/tex] and [tex]\((2x^3 - 4x^2)\)[/tex] is [tex]\(9x^3 - 8x^2\)[/tex].
