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Answer :
To find the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], we need to add the like terms from both polynomials.
1. Identify and Add the [tex]\(x^3\)[/tex] Terms:
- From the first polynomial, the coefficient of [tex]\(x^3\)[/tex] is 7.
- From the second polynomial, the coefficient of [tex]\(x^3\)[/tex] is 2.
- Add these coefficients together: [tex]\(7 + 2 = 9\)[/tex].
- The combined term for [tex]\(x^3\)[/tex] is [tex]\(9x^3\)[/tex].
2. Identify and Add the [tex]\(x^2\)[/tex] Terms:
- From the first polynomial, the coefficient of [tex]\(x^2\)[/tex] is [tex]\(-4\)[/tex].
- From the second polynomial, the coefficient of [tex]\(x^2\)[/tex] is also [tex]\(-4\)[/tex].
- Add these coefficients together: [tex]\(-4 + (-4) = -8\)[/tex].
- The combined term for [tex]\(x^2\)[/tex] is [tex]\(-8x^2\)[/tex].
3. Write the Resulting Polynomial:
- Combine the results from the above steps to form the final polynomial: [tex]\(9x^3 - 8x^2\)[/tex].
Thus, the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex] is [tex]\(\boxed{9x^3 - 8x^2}\)[/tex].
1. Identify and Add the [tex]\(x^3\)[/tex] Terms:
- From the first polynomial, the coefficient of [tex]\(x^3\)[/tex] is 7.
- From the second polynomial, the coefficient of [tex]\(x^3\)[/tex] is 2.
- Add these coefficients together: [tex]\(7 + 2 = 9\)[/tex].
- The combined term for [tex]\(x^3\)[/tex] is [tex]\(9x^3\)[/tex].
2. Identify and Add the [tex]\(x^2\)[/tex] Terms:
- From the first polynomial, the coefficient of [tex]\(x^2\)[/tex] is [tex]\(-4\)[/tex].
- From the second polynomial, the coefficient of [tex]\(x^2\)[/tex] is also [tex]\(-4\)[/tex].
- Add these coefficients together: [tex]\(-4 + (-4) = -8\)[/tex].
- The combined term for [tex]\(x^2\)[/tex] is [tex]\(-8x^2\)[/tex].
3. Write the Resulting Polynomial:
- Combine the results from the above steps to form the final polynomial: [tex]\(9x^3 - 8x^2\)[/tex].
Thus, the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex] is [tex]\(\boxed{9x^3 - 8x^2}\)[/tex].
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