Answer :
To find the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], we can follow these steps:
1. Identify Like Terms:
- In each polynomial, we have terms with [tex]\(x^3\)[/tex] and terms with [tex]\(x^2\)[/tex].
- Polynomial 1: [tex]\(7x^3 - 4x^2\)[/tex]
- Polynomial 2: [tex]\(2x^3 - 4x^2\)[/tex]
2. Add the Coefficients of Like Terms:
- For [tex]\(x^3\)[/tex] terms:
- Add the coefficients of [tex]\(x^3\)[/tex] from both polynomials: [tex]\(7 + 2 = 9\)[/tex].
- For [tex]\(x^2\)[/tex] terms:
- Add the coefficients of [tex]\(x^2\)[/tex] from both polynomials: [tex]\(-4 + (-4) = -8\)[/tex].
3. Write the Resultant Polynomial:
- Combine the results from step 2 to form the new polynomial:
- The sum 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]\(9x^3 - 8x^2\)[/tex].
1. Identify Like Terms:
- In each polynomial, we have terms with [tex]\(x^3\)[/tex] and terms with [tex]\(x^2\)[/tex].
- Polynomial 1: [tex]\(7x^3 - 4x^2\)[/tex]
- Polynomial 2: [tex]\(2x^3 - 4x^2\)[/tex]
2. Add the Coefficients of Like Terms:
- For [tex]\(x^3\)[/tex] terms:
- Add the coefficients of [tex]\(x^3\)[/tex] from both polynomials: [tex]\(7 + 2 = 9\)[/tex].
- For [tex]\(x^2\)[/tex] terms:
- Add the coefficients of [tex]\(x^2\)[/tex] from both polynomials: [tex]\(-4 + (-4) = -8\)[/tex].
3. Write the Resultant Polynomial:
- Combine the results from step 2 to form the new polynomial:
- The sum 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]\(9x^3 - 8x^2\)[/tex].
