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Answer :
To find the sum of the given polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], we need to combine like terms. Let's go through this step-by-step:
1. Identify the Like Terms:
- The terms involving [tex]\(x^3\)[/tex] are [tex]\(7x^3\)[/tex] and [tex]\(2x^3\)[/tex].
- The terms involving [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: Add the coefficients 7 and 2, which gives you [tex]\(9x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms: Add the coefficients [tex]\(-4\)[/tex] and [tex]\(-4\)[/tex], which gives you [tex]\(-8x^2\)[/tex].
3. Write the Resulting Polynomial:
- Combine the results from the above additions to form the new polynomial: [tex]\(9x^3 - 8x^2\)[/tex].
Thus, the sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
1. Identify the Like Terms:
- The terms involving [tex]\(x^3\)[/tex] are [tex]\(7x^3\)[/tex] and [tex]\(2x^3\)[/tex].
- The terms involving [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: Add the coefficients 7 and 2, which gives you [tex]\(9x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms: Add the coefficients [tex]\(-4\)[/tex] and [tex]\(-4\)[/tex], which gives you [tex]\(-8x^2\)[/tex].
3. Write the Resulting Polynomial:
- Combine the results from the above additions to form the new polynomial: [tex]\(9x^3 - 8x^2\)[/tex].
Thus, the sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
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