Answer :
To find the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], we need to combine like terms. Here’s how you can do it step-by-step:
1. Identify Like Terms:
- Look at each term in both polynomials. The terms with [tex]\(x^3\)[/tex] are [tex]\(7x^3\)[/tex] and [tex]\(2x^3\)[/tex].
- The terms with [tex]\(x^2\)[/tex] are [tex]\(-4x^2\)[/tex] and [tex]\(-4x^2\)[/tex].
2. Add the Coefficients of Like Terms:
- For the [tex]\(x^3\)[/tex] terms: [tex]\(7 + 2 = 9\)[/tex]. So, the combined term is [tex]\(9x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms: [tex]\(-4 + (-4) = -8\)[/tex]. So, the combined term is [tex]\(-8x^2\)[/tex].
3. Write the Resulting Polynomial:
- After combining the like terms, the sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
Hence, the sum of the given polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
1. Identify Like Terms:
- Look at each term in both polynomials. The terms with [tex]\(x^3\)[/tex] are [tex]\(7x^3\)[/tex] and [tex]\(2x^3\)[/tex].
- The terms with [tex]\(x^2\)[/tex] are [tex]\(-4x^2\)[/tex] and [tex]\(-4x^2\)[/tex].
2. Add the Coefficients of Like Terms:
- For the [tex]\(x^3\)[/tex] terms: [tex]\(7 + 2 = 9\)[/tex]. So, the combined term is [tex]\(9x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms: [tex]\(-4 + (-4) = -8\)[/tex]. So, the combined term is [tex]\(-8x^2\)[/tex].
3. Write the Resulting Polynomial:
- After combining the like terms, the sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
Hence, the sum of the given polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
